<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, 2000

                                       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, 2000, the number of shares outstanding of the issuer's only
class of stock was 7,547,292 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, 2000    MARCH 31, 2000
                                                              -------------    --------------
<S>                                                           <C>              <C>
CURRENT ASSETS
  Cash and cash equivalents.................................  $       2,733    $      443,818
  Accounts receivable, less allowance for doubtful accounts
     ($7,276 at June 30, 2000 and March 31, 2000,
     respectively)..........................................     12,000,921        13,533,550
  Inventories -- Note B.....................................     25,834,823        22,910,509
  Prepaid expenses and other current assets.................        145,218            57,501
                                                              -------------    --------------
          Total Current Assets..............................     37,983,695        36,945,378
PROPERTY, PLANT AND EQUIPMENT
  Land......................................................        221,543           221,543
  Buildings and improvements................................      3,346,912         3,346,912
  Machinery and equipment...................................     16,170,435        16,075,816
  Less allowance for depreciation...........................    (12,413,737)      (12,170,191)
                                                              -------------    --------------
                                                                  7,325,153         7,474,080
OTHER ASSETS
  Cash value of officers' life insurance....................        883,197           687,332
                                                              -------------    --------------
                                                              $  46,192,045    $   45,106,790
                                                              =============    ==============

LIABILITIES AND STOCKHOLDERS' EQUITY

CURRENT LIABILITIES
  Trade accounts payable and accrued expenses...............  $   7,248,732    $    6,447,538
  Current portion of long-term debt.........................        800,000           800,000
  Dividends payable.........................................        301,950           287,522
  Contribution to profit-sharing plan.......................         69,000           274,000
  Income taxes payable......................................        408,369           256,906
  Employee compensation and related expenses................        318,493           311,313
                                                              -------------    --------------
          Total Current Liabilities.........................      9,146,544         8,377,279
LONG-TERM DEBT, less current portion........................      7,400,000         7,600,000
PROVISION FOR NONPENSION RETIREMENT BENEFITS................        113,000           113,000
DEFERRED INCOME TAXES.......................................        407,060           393,560
STOCKHOLDERS' EQUITY
Common stock:
  Par value $1 per share:
     Authorized 10,000,000 shares; Issued and outstanding
       shares -- 7,547,292 at June 30, 2000 and 7,188,213 at
       March 31, 2000.......................................      7,547,292         7,188,213
  Additional paid-in capital................................     27,685,588        26,878,477
  Retained earnings.........................................     (6,107,439)       (5,443,739)
                                                              -------------    --------------
          Total Stockholders' Equity........................     29,125,441        28,622,951
                                                              -------------    --------------
                                                              $  46,192,045    $   45,106,790
                                                              =============    ==============
</TABLE>

                                        1
<PAGE>   3

                       FRIEDMAN INDUSTRIES, INCORPORATED

                CONSOLIDATED STATEMENTS OF EARNINGS -- UNAUDITED

<TABLE>
<CAPTION>
                                                              THREE MONTHS ENDED JUNE 30,
                                                              ----------------------------
                                                                  2000            1999
                                                              ------------    ------------
<S>                                                           <C>             <C>
Net sales...................................................  $32,274,930     $26,664,262
Costs and expenses
  Costs of goods sold.......................................   29,681,631      24,510,941
  General, selling and administrative costs.................    1,267,811       1,150,970
  Interest..................................................      164,869         137,711
                                                              -----------     -----------
                                                               31,114,311      25,799,622
Interest and other income...................................      (59,862)        (44,680)
                                                              -----------     -----------
Earnings before federal income taxes........................    1,220,481         909,320
Provision (benefit) for federal income taxes:
  Current...................................................      401,463         293,169
  Deferred..................................................       13,500          16,000
                                                              -----------     -----------
                                                                  414,963         309,169
                                                              -----------     -----------
Net earnings................................................  $   805,518     $   600,151
                                                              ===========     ===========
Average number of common shares outstanding:
  Basic.....................................................    7,547,292       7,543,895
  Diluted...................................................    7,547,292       7,543,895
Net earnings per share:
  Basic.....................................................  $      0.11     $      0.08
  Diluted...................................................  $      0.11     $      0.08

Cash dividends declared per common share....................  $      0.04     $      0.05
</TABLE>

                                        2
<PAGE>   4

                       FRIEDMAN INDUSTRIES, INCORPORATED

               CONSOLIDATED STATEMENTS OF CASH FLOWS -- UNAUDITED

<TABLE>
<CAPTION>
                                                              THREE MONTHS ENDED JUNE 30,
                                                              ----------------------------
                                                                  2000            1999
                                                              ------------    ------------
<S>                                                           <C>             <C>
OPERATING ACTIVITIES
  Net earnings..............................................  $   805,518     $   600,151
  Adjustments to reconcile net income to cash provided by
     operating activities:
     Depreciation...........................................      259,725         259,200
     Provision for deferred taxes...........................       13,500          16,000
  Decrease (increase) in operating assets:
     Accounts receivable....................................    1,532,629      (1,086,576)
     Inventories............................................   (2,924,314)        411,215
     Other current assets...................................      (87,717)       (191,925)
  Increase (decrease) in operating liabilities:
     Accounts payable and accrued expenses..................      801,194         346,992
     Contribution to profit-sharing plan payable............     (205,000)       (189,000)
     Employee compensation and related expenses.............        7,180         (15,779)
     Federal income taxes payable...........................      151,463         249,169
                                                              -----------     -----------
NET CASH PROVIDED (USED) BY OPERATING ACTIVITIES............      354,178         399,447
INVESTING ACTIVITIES
  Purchase of property, plant and equipment.................     (110,797)        (83,025)
  Increase in cash surrender value of officers' life
     insurance..............................................      (23,827)         (6,879)
                                                              -----------     -----------
          NET CASH USED IN INVESTING ACTIVITIES.............     (134,624)        (89,904)
FINANCING ACTIVITIES
  Cash dividends paid.......................................     (288,601)       (410,563)
  Principal payments on long-term debt......................     (200,000)     (2,200,000)
  Payments on loans against life insurance..................     (172,038)       (217,715)
  Cash received from exercised stock options................           --          50,068
                                                              -----------     -----------
          NET CASH PROVIDED (USED) IN FINANCING
             ACTIVITIES.....................................     (660,639)     (2,778,210)
                                                              -----------     -----------
INCREASE (DECREASE) IN CASH AND CASH EQUIVALENTS............     (441,085)     (2,468,667)
  Cash and cash equivalents at beginning of period..........      443,818       3,798,935
                                                              -----------     -----------
CASH AND CASH EQUIVALENTS AT END OF PERIOD..................  $     2,733     $ 1,330,268
                                                              ===========     ===========
</TABLE>

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<PAGE>   5

                       FRIEDMAN INDUSTRIES, INCORPORATED

                     NOTES TO QUARTERLY REPORT -- UNAUDITED
                        THREE MONTHS ENDED JUNE 30, 2000

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, 2000.

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, 2000, the Company repaid $172,038 in
borrowings against the cash surrender value of officers' life insurance ("CSV"),
which had the effect of increasing CSV by such amount.

NOTE D -- SEGMENT INFORMATION

<TABLE>
<CAPTION>
                                                              THREE MONTHS ENDED
                                                                   JUNE 30,
                                                              ------------------
                                                               2000       1999
                                                              -------    -------
                                                                 IN THOUSANDS
<S>                                                           <C>        <C>
Net sales
  Coil processing...........................................  $19,911    $18,801
  Tubular...................................................   12,364      7,863
                                                              -------    -------
          Total net sales...................................  $32,275    $26,664
                                                              =======    =======
Operating profit
  Coil processing...........................................  $   317    $ 1,105
  Tubular...................................................    1,717        541
                                                              -------    -------
          Total operating profit............................    2,034      1,646
  Corporate expenses........................................      709        644
  Interest expense..........................................      165        138
  Interest & other income...................................      (60)       (45)
                                                              -------    -------
          Total earnings before taxes.......................  $ 1,220    $   909
                                                              =======    =======
Segment assets
  Coil processing...........................................  $26,987    $23,570
  Tubular...................................................   18,174     14,047
                                                              -------    -------
                                                               45,161     37,617
  Corporate assets..........................................    1,031      1,853
                                                              -------    -------
          Total assets......................................  $46,192    $39,470
                                                              =======    =======
</TABLE>

                                        4
<PAGE>   6

                       FRIEDMAN INDUSTRIES, INCORPORATED

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

 THREE MONTHS ENDED JUNE 30, 2000 COMPARED TO THREE MONTHS ENDED JUNE 30, 1999

     During the quarter ended June 30, 2000, sales, costs of goods sold and
gross profit increased $5,610,668, $5,170,690 and $439,978, respectively, from
the comparable amounts recorded during the quarter ended June 30, 1999. The
increases in sales and costs of goods sold were primarily related to the
Company's tubular operations. During the 2000 quarter, tubular operations
benefited from improved demand for tubular and pipe products and recorded a 47%
increase in tons sold. Gross profit earned on coil sales declined significantly
during the 2000 quarter but was offset by an increase in gross profit earned on
tubular sales. Coil operations were adversely affected by soft market conditions
which produced intense competition for available sales. A decline in margins
earned on coil sales was offset by an increase in margins earned on tubular
sales. During each of the quarters, gross profit as a percentage of sales was
approximately 8%.

     General, selling and administrative costs increased $116,841 from the
amount recorded during the 1999 quarter. This increase was primarily related to
variable expenses attributable to volume and/or earnings and to an increase in
bad debt expense.

     Interest expense increased $27,158 from the amount recorded during the 1999
quarter. This increase was primarily related to an increase in debt associated
with working capital requirements.

     Interest and other income increased $15,182 due primarily to increases in
the average invested cash positions during the 2000 quarter.

     Federal income taxes during the 2000 quarter increased $105,794 from the
comparable amount recorded during the 1999 quarter. This increase was related to
the increase in earnings before taxes as the effective tax rates were the same
for both quarters.

FINANCIAL POSITION, LIQUIDITY AND CAPITAL RESOURCES

     The Company remained in a strong, liquid position at June 30, 2000. Current
ratios were 4.2 and 4.4 at June 30, 2000 and March 31, 2000, respectively.
Working capital was $28,837,151 at June 30, 2000 and $28,568,099 at March 31,
2000.

     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, 2000, the Company had borrowings
outstanding under the revolving facility of $6 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, 2000, the principal
amount of indebtedness outstanding under the term facility was $2.2 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 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

                                        5
<PAGE>   7

results and trends in the future may differ materially depending on a variety of
factors including but not limited to 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.

ITEM 3. QUANTITATIVE AND QUALITATIVE DISCLOSURES ABOUT MARKET RISK

     Not material.

                                        6
<PAGE>   8

                       FRIEDMAN INDUSTRIES, INCORPORATED
                          QUARTER ENDED JUNE 30, 2000

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

Date August 11, 2000                        By      /s/  HAROLD FRIEDMAN
                                            ------------------------------------
                                              Harold Friedman, Vice Chairman of
                                                         the Board

                                        8
<PAGE>   10

                               INDEX TO EXHIBITS

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