<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 JUNE 30, 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 June 30, 1999, the number of shares outstanding of the issuer's only
class of stock was 7,184,662 shares of Common Stock.
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<PAGE>   2

                        PART I -- FINANCIAL INFORMATION

                       FRIEDMAN INDUSTRIES, INCORPORATED
                    CONSOLIDATED BALANCE SHEETS -- UNAUDITED

                                     ASSETS

<TABLE>
<CAPTION>
                                                              JUNE 30, 1999    MARCH 31, 1999
                                                              -------------    --------------
<S>                                                           <C>              <C>
CURRENT ASSETS
  Cash and cash equivalents.................................  $   1,330,268    $    3,798,935
  Accounts receivable, less allowance for doubtful accounts
     ($7,276 at June 30, 1999 and March 31, 1999,
     respectively)..........................................      9,796,304         8,709,728
  Inventories -- Note B.....................................     19,494,955        19,906,170
  Prepaid expenses and other current assets.................        311,132           119,207
                                                              -------------    --------------
          Total Current Assets..............................     30,932,659        32,534,040
PROPERTY, PLANT AND EQUIPMENT
  Land......................................................        221,543           221,543
  Buildings and improvements................................      3,346,912         3,317,088
  Machinery and equipment...................................     15,933,005        15,879,803
  Less allowance for depreciation...........................    (11,386,289)      (11,127,089)
                                                              -------------    --------------
                                                                  8,115,171         8,291,345
OTHER ASSETS
  Cash value of officers' life insurance....................        422,586           197,992
                                                              -------------    --------------
                                                              $  39,470,416    $   41,023,377
                                                              =============    ==============

LIABILITIES AND STOCKHOLDERS' EQUITY

CURRENT LIABILITIES
  Trade accounts payable and accrued expenses...............  $   5,186,552    $    4,839,560
  Current portion of long-term debt.........................        800,000           800,000
  Dividends payable.........................................        359,226           410,563
  Contribution to profit-sharing plan.......................         63,000           252,000
  Income taxes payable......................................        317,691            68,522
  Employee compensation and related expenses................        371,614           387,393
                                                              -------------    --------------
          Total Current Liabilities.........................      7,098,083         6,758,038
LONG-TERM DEBT, less current portion........................      4,200,000         6,400,000
PROVISION FOR NONPENSION RETIREMENT BENEFITS................        113,000           113,000
DEFERRED INCOME TAXES.......................................        345,560           329,560
STOCKHOLDERS' EQUITY
Common stock:
  Par value $1 per share:
     Authorized 10,000,000 shares; Issued and outstanding
       shares -- 7,184,662 at June 30, 1999 and 6,828,387 at
       March 31, 1999.......................................      7,184,662         6,828,387
  Additional paid-in capital................................     26,870,918        25,725,195
  Retained earnings.........................................     (6,341,807)       (5,130,803)
                                                              -------------    --------------
          Total Stockholders' Equity........................     27,713,773        27,422,779
                                                              -------------    --------------
                                                              $  39,470,416        41,023,377
                                                              =============    ==============
</TABLE>

                                        1
<PAGE>   3

                       FRIEDMAN INDUSTRIES, INCORPORATED

                CONSOLIDATED STATEMENTS OF EARNINGS -- UNAUDITED

<TABLE>
<CAPTION>
                                                              THREE MONTHS ENDED JUNE 30,
                                                              ----------------------------
                                                                  1999            1998
                                                              ------------    ------------
<S>                                                           <C>             <C>
Net sales...................................................  $26,664,262     $38,923,169
Costs and expenses
  Costs of goods sold.......................................   24,510,941      36,001,776
  General, selling and administrative costs.................    1,150,970       1,308,234
  Interest..................................................      137,711         102,722
                                                              -----------     -----------
                                                               25,799,622      37,412,732
Interest and other income...................................      (44,680)        (39,181)
                                                              -----------     -----------
Earnings before federal income taxes........................      909,320       1,549,618
Provision (benefit) for federal income taxes:
  Current...................................................      293,169         541,870
  Deferred..................................................       16,000         (15,000)
                                                              -----------     -----------
                                                                  309,169         526,870
                                                              -----------     -----------
Net earnings................................................  $   600,151     $ 1,022,748
                                                              ===========     ===========
Average number of common shares outstanding:
  Basic.....................................................    7,184,662       7,159,949
  Diluted...................................................    7,184,662       7,306,673
Net earnings per share:
  Basic.....................................................  $       .08     $      0.14
  Diluted...................................................  $       .08     $      0.14

Cash dividends declared per common share....................  $       .05     $     0.075
</TABLE>

                                        2
<PAGE>   4

                       FRIEDMAN INDUSTRIES, INCORPORATED

               CONSOLIDATED STATEMENTS OF CASH FLOWS -- UNAUDITED

<TABLE>
<CAPTION>
                                                              THREE MONTHS ENDED JUNE 30,
                                                              ----------------------------
                                                                  1999            1998
                                                              ------------    ------------
<S>                                                           <C>             <C>
OPERATING ACTIVITIES
  Net earnings..............................................  $   600,151     $ 1,022,748
  Adjustments to reconcile net income to cash provided by
     operating activities:
     Depreciation...........................................      259,200         172,476
     Provision for deferred taxes...........................       16,000         (15,000)
  Decrease (increase) in operating assets:
     Accounts receivable....................................   (1,086,576)       (795,891)
     Inventories............................................      411,215         456,738
     Other current assets...................................     (191,925)        (53,317)
  Increase (decrease) in operating liabilities:
     Accounts payable and accrued expenses..................      346,992      (1,133,397)
     Contribution to profit-sharing plan payable............     (189,000)       (209,800)
     Employee compensation and related expenses.............      (15,779)       (103,493)
     Federal income taxes payable...........................      249,169         231,870
                                                              -----------     -----------
NET CASH PROVIDED (USED) BY OPERATING ACTIVITIES............      399,447        (427,066)
INVESTING ACTIVITIES
  Purchase of property, plant and equipment.................      (83,025)       (948,639)
  Increase in cash surrender value of officers' life
     insurance..............................................     (224,594)        (38,563)
                                                              -----------     -----------
          NET CASH USED IN INVESTING ACTIVITIES.............     (307,619)       (987,202)
FINANCING ACTIVITIES
  Cash dividends paid.......................................     (410,563)       (489,660)
  Principal payments on long-term debt......................   (2,200,000)       (200,000)
  Proceeds from borrowings of long-term debt................           --         833,333
  Cash received from exercised stock options................       50,068           5,262
                                                              -----------     -----------
          NET CASH PROVIDED (USED) IN FINANCING
             ACTIVITIES.....................................   (2,560,495)        148,935
                                                              -----------     -----------
INCREASE (DECREASE) IN CASH AND CASH EQUIVALENTS............   (2,468,667)     (1,265,333)
  Cash and cash equivalents at beginning of period..........    3,798,935       1,361,693
                                                              -----------     -----------
CASH AND CASH EQUIVALENTS AT END OF PERIOD..................  $ 1,330,268     $    96,360
                                                              ===========     ===========
</TABLE>

                                        3
<PAGE>   5

                       FRIEDMAN INDUSTRIES, INCORPORATED

                     NOTES TO QUARTERLY REPORT -- UNAUDITED
                        THREE MONTHS ENDED JUNE 30, 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 quarter ended June 30, 1999, the Company repaid borrowings
against the cash surrender value of officers' life insurance ("CSV"). A total of
$217,715 was repaid which had the effect of increasing CSV by such amount.

NOTE D -- SEGMENT INFORMATION

<TABLE>
<CAPTION>
                                                              THREE MONTHS ENDED
                                                                   JUNE 30,
                                                              ------------------
                                                               1999       1998
                                                              -------    -------
                                                                (IN THOUSANDS)
<S>                                                           <C>        <C>
Net sales
  Coil processing...........................................  $18,801    $25,252
  Tubular...................................................    7,863     13,671
                                                              -------    -------
          Total net sales...................................  $26,664    $38,923
                                                              =======    =======
Operating profit
  Coil processing...........................................  $ 1,105    $ 1,140
  Tubular...................................................      541      1,167
                                                              -------    -------
          Total operating profit............................    1,646      2,307
  Corporate expenses........................................      644        693
  Interest expense..........................................      138        103
  Interest & other income...................................      (45)       (39)
                                                              -------    -------
          Total earnings before taxes.......................  $   909    $ 1,550
                                                              =======    =======
Segment assets
  Coil processing...........................................  $23,570    $28,500
  Tubular...................................................   14,047     17,226
                                                              -------    -------
                                                               37,617     45,726
  Corporate assets..........................................    1,853        255
                                                              -------    -------
          Total assets......................................  $39,470    $45,981
                                                              =======    =======
</TABLE>

                                        4
<PAGE>   6

                       FRIEDMAN INDUSTRIES, INCORPORATED

                    MANAGEMENT'S DISCUSSION AND ANALYSIS OF
                 FINANCIAL CONDITION AND RESULTS OF OPERATIONS

 THREE MONTHS ENDED JUNE 30, 1999 COMPARED TO THREE MONTHS ENDED JUNE 30, 1998

     During the quarter ended June 30, 1999, sales, costs of goods sold and
gross profit declined $12,258,907, $11,490,835 and $768,072, respectively, from
the comparable amounts recorded during the quarter ended June 30, 1998. The
declines in sales and costs of goods sold were related to both coil and tubular
operations. Sales of coil products declined approximately 25% due to a decrease
in tons sold and a decline in the average per ton selling price. The decrease in
tons sold of coil products was primarily related to the market demand for these
products, and the decline in the average per ton selling price was primarily a
reflection of reduced costs of coil products. Sales of tubular products declined
approximately 42% due primarily to a decline in volume. Soft demand for tubular
products continued to generate intense competition for available sales during
the 1999 quarter. The decline in gross profit was primarily related to the
decrease in tubular sales described above. Gross profit as a percentage of sales
increased from 7.5% during the 1998 quarter to 8.1% during the 1999 quarter. A
decline in margins earned on tubular sales was more than offset by an
improvement in margins earned on coil sales.

     General, selling and administrative costs in the 1999 quarter declined
$157,264 from the amount recorded during the 1998 quarter. This decline was
primarily related to variable expenses associated with reduced volume and
earnings.

     Interest expense in the 1999 quarter increased $34,989 from the amount
recorded in the 1998 quarter. During the 1999 quarter, the Company began
operating a temper pass mill at its Arkansas coil facility. Interest on the term
debt associated with this asset was capitalized in the 1998 quarter and was
expensed in the 1999 quarter.

     Federal income taxes declined $217,701 as a result of the decrease in
earnings before tax. The effective tax rate was the same for both quarters.

FINANCIAL POSITION, LIQUIDITY AND CAPITAL RESOURCES

     The Company remained in a strong, liquid position at June 30, 1999. Current
ratios were 4.4 and 4.8 at June 30, 1999 and March 31, 1999, respectively.
Working capital was $23,834,576 at June 30, 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 June 30, 1999, the Company had borrowings
outstanding under the revolving facility of $2 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 June 30, 1999, the principal
amount of indebtedness outstanding under the term facility was $3 million.

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

                                        5
<PAGE>   7

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 suppliers, third party payors and
customers, having 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.

     In 1998, the Company completed an assessment of the readiness of its
internal computer systems and related applications to accommodate date-sensitive
information relating to the year 2000 and developed a plan to resolve all major
issues by the end of 1999. As a result, the Year 2000 issue is not expected to
pose significant operational or financial problems for the Company.

     The Company will continue to analyze systems and services that utilize
date-embedded codes that may experience operational problems when the year 2000
is reached. The Company will continue to communicate with its suppliers,
third-party payors and customers to coordinate Year 2000 compliance. Because the
ability of these third parties to address their Year 2000 issues is outside the
Company's control, the failure of third parties to adequately address their
respective Year 2000 issues may have a material adverse effect on the Company's
results of operations and financial condition.

     The foregoing statements are intended to be and are hereby 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.

                                        6
<PAGE>   8

                       FRIEDMAN INDUSTRIES, INCORPORATED
                          QUARTER ENDED JUNE 30, 1999

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

<TABLE>
<C>                      <S>
         10.1            -- Third Amendment to the Amended and Restated Letter
                            Agreement dated April 1, 1999 between the Company and
                            Chase Bank of Texas ("Chase")
         10.2            -- Revolving Promissory Note dated April 1, 1999 between the
                            Company and Chase
         27.1            -- Financial Data Schedule
</TABLE>

     b). Reports on Form 8-K

          None

                                        7
<PAGE>   9

                                   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 August 13, 1999                        By        /s/  BEN HARPER

                                            ------------------------------------
                                                  Ben Harper, Senior Vice
                                                     President-Finance
                                                 (Chief Accounting Officer)

Date August 13, 1999                        By      /s/  HAROLD FRIEDMAN

                                            ------------------------------------
                                              Harold Friedman, Vice Chairman of
                                                         the Board

                                        8
<PAGE>   10

                               INDEX TO EXHIBITS

<TABLE>
<CAPTION>
        EXHIBIT
         NUMBER                                  DESCRIPTION
        -------                                  -----------
<C>                      <S>
         10.1            -- Third Amendment to Amended and Restated Letter Agreement.
         10.2            -- Revolving Promissory Note.
         27.1            -- Financial Data Schedule.
</TABLE>