<PAGE>   1

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                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                   FORM 10-Q

[X] QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE
    ACT OF 1934 FOR THE QUARTERLY PERIOD ENDED DECEMBER 31, 1999

                                       OR

[ ] TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE
    ACT OF 1934 FROM THE TRANSITION PERIOD FROM                   TO

                         COMMISSION FILE NUMBER 1-7521

                       FRIEDMAN INDUSTRIES, INCORPORATED
             (Exact name of registrant as specified in its charter)

<TABLE>
<S>                                            <C>
                    TEXAS                                             74-1504405
       (State or other jurisdiction of                     (I.R.S. Employer Identification
        incorporation or organization)                                 Number)
</TABLE>

                 4001 HOMESTEAD ROAD, HOUSTON, TEXAS 77028-5585
                (Address of principal executive office zip code)
       Registrant's telephone number, including area code (713) 672-9433

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Former name, former address and former fiscal year, if changed since last report

     Indicate by check mark whether the registrant (1) has filed all reports
required to be filed by Section 13 or 15(d) of the Securities Exchange Act of
1934 during the preceding 12 months, and (2) has been subject to such filing
requirements for the past 90 days.

                               Yes  X     No

     At December 31, 1999, the number of shares outstanding of the issuer's only
class of stock was 7,188,213 shares of Common Stock.
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<PAGE>   2

                        PART I -- FINANCIAL INFORMATION

                       FRIEDMAN INDUSTRIES, INCORPORATED

ITEM 1. FINANCIAL STATEMENTS

                    CONSOLIDATED BALANCE SHEETS -- UNAUDITED

                                     ASSETS

<TABLE>
<CAPTION>
                                                              DECEMBER 31, 1999   MARCH 31, 1999
                                                              -----------------   --------------
<S>                                                           <C>                 <C>
CURRENT ASSETS
  Cash and cash equivalents.................................    $    136,478       $  3,798,935
  Accounts receivable, less allowance for doubtful accounts
     ($7,276 at December 31, 1999 and March 31, 1999,
     respectively)..........................................      10,392,403          8,709,728
  Inventories -- Note B.....................................      26,695,416         19,906,170
  Prepaid expenses and other current assets.................         167,733            119,207
                                                                ------------       ------------
          Total Current Assets..............................      37,392,030         32,534,040
PROPERTY, PLANT AND EQUIPMENT
  Land......................................................         221,543            221,543
  Buildings and improvements................................       3,346,911          3,317,088
  Machinery and equipment...................................      16,031,180         15,879,803
  Less allowance for depreciation...........................     (11,908,688)       (11,127,089)
                                                                ------------       ------------
                                                                   7,690,946          8,291,345
OTHER ASSETS
  Cash value of officers' life insurance....................         625,081            197,992
                                                                ------------       ------------
                                                                $ 45,708,057       $ 41,023,377
                                                                ============       ============

LIABILITIES AND STOCKHOLDERS' EQUITY

CURRENT LIABILITIES
  Trade accounts payable and accrued expenses...............    $  8,642,408       $  4,839,560
  Current portion of long-term debt.........................         800,000            800,000
  Dividends payable.........................................         359,403            410,563
  Contribution to profit-sharing plan.......................         189,000            252,000
  Income taxes payable......................................              --             68,522
  Employee compensation and related expenses................         183,256            387,393
                                                                ------------       ------------
          Total Current Liabilities.........................      10,174,067          6,758,038
LONG-TERM DEBT, less current portion........................       6,800,000          6,400,000
PROVISION FOR NONPENSION RETIREMENT BENEFITS................         113,000            113,000
DEFERRED INCOME TAXES.......................................         377,560            329,560
STOCKHOLDERS' EQUITY
Common stock:
  Par value $1 per share:
     Authorized 10,000,000 shares; Issued and outstanding
       shares -- 7,188,213 at December 31, 1999 and
       6,828,387 at
       March 31, 1999.......................................       7,188,213          6,828,387
  Additional paid-in capital................................      26,877,738         25,725,195
  Retained deficit..........................................      (5,822,521)        (5,130,803)
                                                                ------------       ------------
          Total Stockholders' Equity........................      28,243,430         27,422,779
                                                                ------------       ------------
                                                                $ 45,708,057       $ 41,023,377
                                                                ============       ============
</TABLE>

                                        1
<PAGE>   3

                       FRIEDMAN INDUSTRIES, INCORPORATED

                CONSOLIDATED STATEMENTS OF EARNINGS -- UNAUDITED

<TABLE>
<CAPTION>
                                              THREE MONTHS ENDED           NINE MONTHS ENDED
                                                 DECEMBER 31,                DECEMBER 31,
                                           -------------------------   -------------------------
                                              1999          1998          1999          1998
                                           -----------   -----------   -----------   -----------
<S>                                        <C>           <C>           <C>           <C>
Net sales................................  $29,894,914   $26,938,495   $85,956,294   $98,039,953
Costs and expenses:
  Costs of goods sold....................   28,010,830    24,806,991    79,639,615    90,119,844
  General, selling and administrative
     costs...............................    1,059,057     1,035,859     3,305,224     3,567,453
  Interest...............................      119,814       112,042       354,870       367,755
                                           -----------   -----------   -----------   -----------
                                            29,189,701    25,954,892    83,299,709    94,055,052
Interest and other income................      (52,698)      (49,277)     (130,811)     (135,603)
                                           -----------   -----------   -----------   -----------
Earnings before federal income taxes.....      757,911     1,032,880     2,787,396     4,120,504
Provision (benefit) for federal income
  taxes:
  Current................................      241,690       366,180       899,716     1,445,972
  Deferred...............................       16,000       (15,000)       48,000       (45,000)
                                           -----------   -----------   -----------   -----------
                                               257,690       351,180       947,716     1,400,972
                                           -----------   -----------   -----------   -----------
Net earnings.............................  $   500,221   $   681,700   $ 1,839,680   $ 2,719,532
                                           ===========   ===========   ===========   ===========
Average number of common shares
  outstanding:
  Basic..................................    7,188,213     7,167,706     7,188,213     7,167,706
  Diluted................................    7,188,213     7,207,145     7,188,213     7,207,145
Net earnings per share:
  Basic..................................  $      0.07   $      0.10   $      0.26   $      0.38
  Diluted................................  $      0.07   $      0.09   $      0.26   $      0.38

Cash dividends declared per common
  share..................................  $      0.05   $      0.07   $      0.15   $     0.215
</TABLE>

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<PAGE>   4

                       FRIEDMAN INDUSTRIES, INCORPORATED

               CONSOLIDATED STATEMENTS OF CASH FLOWS -- UNAUDITED

<TABLE>
<CAPTION>
                                                                  NINE MONTHS ENDED
                                                                     DECEMBER 31,
                                                              --------------------------
                                                                 1999           1998
                                                              -----------    -----------
<S>                                                           <C>            <C>
OPERATING ACTIVITIES
  Net earnings..............................................  $ 1,839,680    $ 2,719,532
  Adjustments to reconcile net earnings to cash provided by
     operating activities:..................................
     Depreciation...........................................      781,600        517,428
     Provision for deferred taxes...........................       48,000        (45,000)
  Decrease (increase) in operating assets:..................
     Accounts receivable....................................   (1,682,675)     4,967,821
     Inventories............................................   (6,789,246)     1,016,823
     Other..................................................      (48,526)      (397,040)
  Increase (decrease) in operating liabilities:.............
     Accounts payable and accrued expenses..................    3,802,848     (6,195,267)
     Contribution to profit-sharing plan....................      (63,000)       (69,400)
     Employee compensation and related expenses.............     (204,137)      (376,837)
     Federal income taxes...................................      (68,522)      (344,465)
                                                              -----------    -----------
          NET CASH PROVIDED (USED) BY OPERATING
             ACTIVITIES.....................................   (2,383,978)     1,793,595
INVESTING ACTIVITIES........................................
  Purchase of property, plant and equipment.................     (181,200)    (1,758,212)
  Decrease (increase) in cash value of officers' life
     insurance..............................................     (427,089)      (112,812)
                                                              -----------    -----------
          NET CASH PROVIDED (USED) IN INVESTING
             ACTIVITIES.....................................     (608,289)    (1,871,024)
FINANCING ACTIVITIES........................................
  Cash dividends paid.......................................   (1,130,628)    (1,478,674)
  Principal payments on long-term debt......................   (2,600,000)    (3,600,000)
  Proceeds from borrowings of long term debt................    3,000,000      3,833,333
  Exercise of stock options.................................       60,438         18,413
                                                              -----------    -----------
          NET CASH PROVIDED (USED) IN FINANCING
             ACTIVITIES.....................................     (670,190)    (1,226,928)
                                                              -----------    -----------
INCREASE (DECREASE) IN CASH AND CASH EQUIVALENTS............   (3,662,457)    (1,304,357)
  Cash and cash equivalents at beginning of period..........    3,798,935      1,361,693
                                                              -----------    -----------
CASH AND CASH EQUIVALENTS AT END OF PERIOD..................  $   136,478    $    57,336
                                                              ===========    ===========
</TABLE>

                                        3
<PAGE>   5

                       FRIEDMAN INDUSTRIES, INCORPORATED

                     NOTES TO QUARTERLY REPORT -- UNAUDITED
                      NINE MONTHS ENDED DECEMBER 31, 1999

NOTE A -- BASIS OF PRESENTATION

     The accompanying unaudited condensed, consolidated financial statements
have been prepared in accordance with the instructions to Form 10-Q and do not
include all of the information and footnotes required by generally accepted
accounting principles for complete financial statements. In the opinion of
management, all adjustments (consisting of normal recurring accruals) considered
necessary for a fair presentation have been included. For further information,
refer to the financial statements and footnotes included in the Company's annual
report on Form 10-K for the year ended March 31, 1999.

NOTE B -- INVENTORIES

     Coil inventory consists primarily of raw materials. Tubular inventory is
comprised of both raw materials and finished goods.

NOTE C -- CASH VALUE OF OFFICERS' LIFE INSURANCE

     During the nine months ended December 31, 1999, the Company repaid
borrowings against the cash surrender value of officers' life insurance ("CSV").
A total of $364,619 was repaid which had the effect of increasing CSV by such
amount.

NOTE D -- SEGMENT INFORMATION

<TABLE>
<CAPTION>
                                                         THREE MONTHS ENDED    NINE MONTHS ENDED
                                                            DECEMBER 31,         DECEMBER 31,
                                                         -------------------   -----------------
                                                           1999       1998      1999      1998
                                                         --------   --------   -------   -------
                                                           (IN THOUSANDS)       (IN THOUSANDS)
<S>                                                      <C>        <C>        <C>       <C>
Net sales
  Coil processing......................................  $18,458    $19,607    $57,186   $66,553
  Tubular..............................................   11,437      7,332     28,770    31,487
                                                         -------    -------    -------   -------
          Total net sales..............................  $29,895    $26,939     85,956   $98,040
                                                         =======    =======    =======   =======
Operating profit
  Coil processing......................................  $   233    $ 1,466      2,345   $ 4,035
  Tubular..............................................    1,030         37      2,278     2,031
                                                         -------    -------    -------   -------
          Total operating profit.......................    1,263      1,503      4,623     6,066
  Corporate expenses...................................      438        408      1,612     1,713
  Interest expense.....................................      120        112        355       368
  Interest & other income..............................      (53)       (50)      (131)     (136)
                                                         -------    -------    -------   -------
          Total earnings before taxes..................  $   758    $ 1,033    $ 2,787   $ 4,121
                                                         =======    =======    =======   =======
</TABLE>

<TABLE>
<CAPTION>
                                                                DECEMBER 31,
                                                              -----------------
                                                               1999      1998
                                                              -------   -------
                                                               (IN THOUSANDS)
<S>                                                           <C>       <C>
Segment assets
  Coil processing...........................................  $28,989   $26,314
  Tubular...................................................   15,858    13,886
                                                              -------   -------
                                                               44,847    40,200
  Corporate assets..........................................      861       301
                                                              -------   -------
          Total assets......................................  $45,708   $40,501
                                                              =======   =======
</TABLE>

                                        4
<PAGE>   6

ITEM 2. MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS
        OF OPERATIONS

 NINE MONTHS ENDED DECEMBER 31, 1999 COMPARED TO NINE MONTHS ENDED DECEMBER 31,
                                      1998

     During the nine months ended December 31,1999, sales, costs of goods sold
and gross profit declined $12,083,659, $10,480,229, and $1,603,430,
respectively, from the comparable amounts recorded during the nine months ended
December 31, 1998. The Company recorded decreased sales in both coil and tubular
product lines. Coil sales were affected by a decline in volume primarily
associated with softer demand for these products. In addition, coil and tubular
sales decreased as the result of an aggregate decline of approximately 11% in
the average selling price per ton. This reduction in average selling price was
primarily associated with reduced costs of coil and tubular products. The
decline in costs of goods sold was principally related to the sales decrease
experienced during the 1999 period. The decrease in gross profit was primarily
associated with the Company's coil operations which were adversely affected by
the decline in volume, softer market conditions and reduced margins earned on
sales. During the quarter ended December 31, 1999, the Company incurred
significant increases in costs of coil products and these costs could not be
immediately passed along to customers.

     Federal income taxes declined $453,256 from the amount recorded during the
1998 period. This decrease was attributable to the decline in earnings before
taxes. Effective tax rates were the same for both periods.

THREE MONTHS ENDED DECEMBER 31, 1999 COMPARED TO THREE MONTHS ENDED DECEMBER 31,
                                      1998

     During the three months ended December 31, 1999, sales and costs of goods
sold increased $2,956,419 and $3,203,839, respectively, from the comparable
amounts recorded during the three months ended December 31, 1998, the effect of
which produced a decline in gross profit of $247,420. The increases in sales and
costs of goods sold were primarily related to increased sales of tubular
products. Market conditions for tubular products improved substantially during
the 1999 quarter. The net decline in gross profit of $247,420 resulted from an
increase in gross profit on tubular operations of $1,021,897 and a decrease in
gross profit on coil operations of $1,269,317. Coil operations were adversely
affected by reduced volume, softer market conditions and reduced margins earned
on sales. During the 1999 quarter, the Company incurred significant increases in
costs of coil products and these costs could not be immediately passed along to
customers.

     Federal income taxes declined $93,490 from the amount recorded during the
1998 quarter. This decrease was attributable to the decline in earnings before
taxes. The effective tax rates were the same for both periods.

FINANCIAL POSITION, LIQUIDITY AND CAPITAL RESOURCES

     The Company remained in a strong, liquid position at December 31, 1999.
Current ratios were 3.7 and 4.8 at December 31, 1999 and March 31, 1999,
respectively. Working capital was $27,217,963 at December 31, 1999 and
$25,776,002 at March 31, 1999.

     The Company has a credit arrangement with a bank which provides for a
revolving line of credit facility (the "revolving facility") and a term credit
facility (the "term facility"). Pursuant to the revolving facility which expires
April 1, 2002, the Company may borrow up to $8 million at an interest rate no
greater than the bank's prime rate. At December 31, 1999, the Company had
borrowings outstanding under the revolving facility of $5 million. The amount
outstanding under the term facility bears interest at a stated rate of LIBOR
plus 1.25% and requires quarterly principal payments of $200,000 plus accrued
interest through March 1, 2003. In July 1997, the Company entered into a swap
transaction with the bank pursuant to which it exchanged the term facility's
LIBOR-based interest rate obligation for a fixed interest rate obligation of 8%
to remain in effect for the entire term of the term facility. As of December 31,
1999, the principal amount of indebtedness outstanding under the term facility
was $2.6 million.

                                        5
<PAGE>   7

FORWARD-LOOKING STATEMENTS

     From time to time, the Company may make certain statements that contain
"forward-looking" information (as defined in the Private Securities Litigation
Reform Act of 1996) and that involve risk and uncertainty. These forward-looking
statements may include, but are not limited to, future results of operations,
future production capacity and product quality. Forward-looking statements may
be made by management orally or in writing including, but not limited to, this
Management's Discussion and Analysis of Financial Condition and Results of
Operations and other sections of the Company's filings with the Securities and
Exchange Commission under the Securities Act of 1933 and the Securities Exchange
Act of 1934. Actual results and trends in the future may differ materially
depending on a variety of factors including but not limited to, the success of
the Company's capital improvements at its Hickman, Arkansas facility, changes in
the demand and prices for the Company's products and changes in the demand for
steel and steel products in general, and the Company's success in executing its
internal operations plans.

EFFECT OF YEAR 2000 ISSUE

     The Year 2000 issue is the result of computer programming being written
using two digits rather than four to define the applicable year. Any of the
Company's systems, as well as those of key vendors, payors and customers, that
have date sensitive logic may interpret a date using "00" as the year 1900
rather than 2000. This may cause inaccurate processing or possible system
failure and may potentially disrupt operations. This disruption may result in,
among other things, a temporary inability to process transactions, send bills
for services or engage in similar normal business activities. The Year 2000
issue did not result in significant operational or financial problems for the
Company. The Company is not aware of any significant problems experienced by its
suppliers, third-party payors or customers as a result of the Year 2000 issue,
but the Company will continue to communicate with such parties regarding any
possible problems. The foregoing statements are intended to be and hereby are
designated "Year 2000 Readiness Disclosure Statements" within the meaning of the
Year 2000 Information and Readiness Disclosure Act.

ITEM 3. QUANTITATIVE AND QUALITATIVE DISCLOSURES ABOUT MARKET RISK

     Not applicable.

                          PART II -- OTHER INFORMATION

ITEM 1. LEGAL PROCEEDINGS

     Not applicable

ITEM 2. CHANGES IN SECURITIES

     a). Not applicable

     b). Not applicable

     c). Not applicable

     d). Not applicable

ITEM 3. DEFAULTS UPON SENIOR SECURITIES

     a). Not applicable

     b). Not applicable

ITEM 4. SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS

     None

ITEM 5. OTHER INFORMATION

     Not applicable

ITEM 6. EXHIBITS AND REPORTS ON FORM 8-K

     a). Exhibits

        27.1 -- Financial Data Schedule

     b). Reports on Form 8-K

          None

                                        6
<PAGE>   8

                                   SIGNATURES

     Pursuant to the requirements of the Securities Exchange Act of 1934, the
registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto duly authorized.

                                            FRIEDMAN INDUSTRIES, INCORPORATED

Date February 11, 2000                      By        /s/  BEN HARPER
                                            ------------------------------------
                                                  Ben Harper, Senior Vice
                                                     President-Finance
                                                 (Chief Accounting Officer)

Date February 11, 2000                      By      /s/  HAROLD FRIEDMAN
                                            ------------------------------------
                                                Harold Friedman, Vice Chairman

                                        7
<PAGE>   9

                               INDEX TO EXHIBITS

<TABLE>
<CAPTION>
        EXHIBIT
         NUMBER                                  DESCRIPTION
        -------                                  -----------
<C>                      <S>
         27.1            -- Financial Data Schedule.
</TABLE>