<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, 2001

                                       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, 2001, the number of shares outstanding of the issuer's only
class of stock was 7,568,839 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, 2001    MARCH 31, 2001
                                                              -------------    --------------
<S>                                                           <C>              <C>
CURRENT ASSETS
  Cash and cash equivalents.................................  $     321,395    $      669,076
  Accounts receivable.......................................      9,820,174        10,584,735
  Inventories -- Note B.....................................     25,351,878        28,817,375
  Prepaid expenses and other current assets.................        219,856           160,143
                                                              -------------    --------------
          Total Current Assets..............................     35,713,303        40,231,329
PROPERTY, PLANT AND EQUIPMENT
  Land......................................................        221,543           221,543
  Buildings and improvements................................      3,346,912         3,346,912
  Machinery and equipment...................................     16,472,700        16,458,899
  Less allowance for depreciation...........................    (13,424,791)      (13,201,590)
                                                              -------------    --------------
                                                                  6,616,364         6,825,764
OTHER ASSETS
  Cash value of officers' life insurance....................        960,338           953,419
                                                              -------------    --------------
                                                              $  43,290,005    $   48,010,512
                                                              =============    ==============

LIABILITIES AND STOCKHOLDERS' EQUITY

CURRENT LIABILITIES
  Trade accounts payable and accrued expenses...............  $   5,955,872    $   10,443,848
  Current portion of long-term debt.........................        800,000           800,000
  Dividends payable.........................................        302,745           302,746
  Contribution to profit-sharing plan.......................         72,000           288,000
  Income taxes payable......................................        220,425           127,209
  Employee compensation and related expenses................        254,401           309,999
                                                              -------------    --------------
          Total Current Liabilities.........................      7,605,443        12,271,802
LONG-TERM DEBT, less current portion........................      4,600,000         4,800,000
PROVISION FOR NONPENSION RETIREMENT BENEFITS................        113,000           113,000
DEFERRED INCOME TAXES.......................................        456,060           447,560
STOCKHOLDERS' EQUITY
Common stock:
  Par value $1 per share:
     Authorized 10,000,000 shares; Issued and outstanding
       shares -- 7,568,839 at June 30, 2001 and March 31,
       2001, respectively...................................      7,568,839         7,568,839
  Additional paid-in capital................................     27,703,829        27,703,829
  Retained deficit..........................................     (4,757,166)       (4,894,518)
                                                              -------------    --------------
          Total Stockholders' Equity........................     30,515,502        30,378,150
                                                              -------------    --------------
                                                              $  43,290,005    $   48,010,512
                                                              =============    ==============
</Table>

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<PAGE>   3

                       FRIEDMAN INDUSTRIES, INCORPORATED

                CONSOLIDATED STATEMENTS OF EARNINGS -- UNAUDITED

<Table>
<Caption>
                                                              THREE MONTHS ENDED JUNE 30,
                                                              ----------------------------
                                                                  2001            2000
                                                              ------------    ------------
<S>                                                           <C>             <C>
Net sales...................................................  $27,885,663     $32,274,930
Costs and expenses
  Costs of goods sold.......................................   26,014,170      29,681,631
  General, selling and administrative costs.................    1,101,246       1,267,811
  Interest..................................................      109,082         164,869
                                                              -----------     -----------
                                                               27,224,498      31,114,311
Interest and other income...................................       (5,648)        (59,862)
                                                              -----------     -----------
Earnings before federal income taxes........................      666,813       1,220,481
Provision (benefit) for federal income taxes:
  Current...................................................      218,216         401,463
  Deferred..................................................        8,500          13,500
                                                              -----------     -----------
                                                                  226,716         414,963
                                                              -----------     -----------
Net earnings................................................  $   440,097     $   805,518
                                                              ===========     ===========
Average number of common shares outstanding:
  Basic.....................................................    7,568,839       7,547,292
  Diluted...................................................    7,568,839       7,547,292
Net earnings per share:
  Basic.....................................................  $      0.06     $      0.11
  Diluted...................................................  $      0.06     $      0.11

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

                                        2
<PAGE>   4

                       FRIEDMAN INDUSTRIES, INCORPORATED

               CONSOLIDATED STATEMENTS OF CASH FLOWS -- UNAUDITED

<Table>
<Caption>
                                                              THREE MONTHS ENDED JUNE 30,
                                                              ----------------------------
                                                                  2001            2000
                                                              ------------    ------------
<S>                                                           <C>             <C>
OPERATING ACTIVITIES
  Net earnings..............................................  $   440,097     $   805,518
  Adjustments to reconcile net income to cash provided by
     operating activities:
     Depreciation...........................................      223,200         259,725
     Provision for deferred taxes...........................        8,500          13,500
  Decrease (increase) in operating assets:
     Accounts receivable....................................      764,561       1,532,629
     Inventories............................................    3,465,497      (2,924,314)
     Other current assets...................................      (59,713)        (87,717)
  Increase (decrease) in operating liabilities:
     Accounts payable and accrued expenses..................   (4,487,976)        801,194
     Contribution to profit-sharing plan payable............     (216,000)       (205,000)
     Employee compensation and related expenses.............      (55,598)          7,180
     Federal income taxes payable...........................       93,216         151,463
                                                              -----------     -----------
NET CASH PROVIDED (USED) BY OPERATING ACTIVITIES............      175,784         354,178
INVESTING ACTIVITIES
  Purchase of property, plant and equipment.................      (13,800)       (110,797)
  Increase in cash surrender value of officers' life
     insurance..............................................       (6,919)        (23,827)
                                                              -----------     -----------
          NET CASH USED IN INVESTING ACTIVITIES.............      (20,719)       (134,624)
FINANCING ACTIVITIES
  Cash dividends paid.......................................     (302,746)       (288,601)
  Principal payments on long-term debt......................     (200,000)       (200,000)
  Payments on loans against life insurance..................           --        (172,038)
                                                              -----------     -----------
          NET CASH PROVIDED (USED) IN FINANCING
             ACTIVITIES.....................................     (502,746)       (660,639)
                                                              -----------     -----------
INCREASE (DECREASE) IN CASH AND CASH EQUIVALENTS............     (347,681)       (441,085)
  Cash and cash equivalents at beginning of period..........      669,076         443,818
                                                              -----------     -----------
CASH AND CASH EQUIVALENTS AT END OF PERIOD..................  $   321,395     $     2,733
                                                              ===========     ===========
</Table>

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<PAGE>   5

                       FRIEDMAN INDUSTRIES, INCORPORATED

                     NOTES TO QUARTERLY REPORT -- UNAUDITED
                        THREE MONTHS ENDED JUNE 30, 2001

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, 2001.

NOTE B -- INVENTORIES

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

NOTE C -- SEGMENT INFORMATION

<Table>
<Caption>
                                                              THREE MONTHS ENDED
                                                                   JUNE 30,
                                                              ------------------
                                                               2001       2000
                                                              -------    -------
                                                                 IN THOUSANDS
<S>                                                           <C>        <C>
Net sales
  Coil processing...........................................  $14,011    $19,911
  Tubular...................................................   13,875     12,364
                                                              -------    -------
          Total net sales...................................  $27,886    $32,275
                                                              =======    =======
Operating profit
  Coil processing (loss)....................................  $   (64)   $   317
  Tubular...................................................    1,400      1,717
                                                              -------    -------
          Total operating profit............................    1,336      2,034
  Corporate expenses........................................      566        709
  Interest expense..........................................      109        165
  Interest & other income...................................       (6)       (60)
                                                              -------    -------
          Total earnings before taxes.......................  $   667    $ 1,220
                                                              =======    =======
Segment assets
  Coil processing...........................................  $18,543    $26,987
  Tubular...................................................   23,169     18,174
                                                              -------    -------
                                                               41,712     45,161
  Corporate assets..........................................    1,578      1,031
                                                              -------    -------
          Total assets......................................  $43,290    $46,192
                                                              =======    =======
</Table>

                                        4
<PAGE>   6

                       FRIEDMAN INDUSTRIES, INCORPORATED

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

 THREE MONTHS ENDED JUNE 30, 2001 COMPARED TO THREE MONTHS ENDED JUNE 30, 2000

     During the quarter ended June 30, 2001, sales, costs of goods sold and
gross profit decreased $4,389,267, $3,667,461 and $721,806, respectively, from
the comparable amounts recorded during the quarter ended June 30, 2000. The
decreases in sales and costs of goods sold were related primarily to the
Company's coil operations. During the 2001 quarter, soft market conditions for
coil products continued to have the effect of generating intense competition for
available sales which adversely affected coil product sales and related gross
profit during the 2001 quarter. Tons of coil products sold declined 12.1% and
the average selling price of such products declined 20.9% from the respective
amounts recorded during the 2000 quarter. Gross profit earned on tubular
products also decreased from the comparable amount recorded during the 2000
quarter. Even though tubular operations recorded an increase of 20.5% in tons
sold, market conditions for tubular products were more competitive in the 2001
quarter and resulted in the decrease noted above.

     General, selling and administrative costs declined $166,565 from the amount
recorded during the 2000 quarter. This decline was associated primarily with
variable expenses related to volume and/or earnings.

     Interest expense decreased $55,787 from the comparable amount recorded
during the 2000 quarter. This decrease was related principally to a reduction in
debt associated with working capital requirements.

     Interest and other income decreased $54,214 primarily as a result of a
decline in invested cash positions and interest rates paid on such positions
during the 2001 quarter.

     Federal income taxes during the 2001 quarter decreased $188,247 from the
comparable amount recorded during the 2000 quarter. This decrease was related to
the decline 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, 2001. Current
ratios were 4.7 and 3.3 at June 30, 2001 and March 31, 2001, respectively.
Working capital was $28,107,860 at June 30, 2001 and $27,959,527 at March 31,
2001. Inventories and trade accounts payable declined $3,465,497 and $4,487,976,
respectively. The Company reduced coil inventories during the quarter ended June
30, 2001 to a level more commensurate with operations. This reduction was the
principal factor in the decrease in trade accounts payable.

     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, 2004, the Company may borrow up to $10 million at an interest rate no
greater than the bank's prime rate. At June 30, 2001, the Company had borrowings
outstanding under the revolving facility of $4 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, 2001, the principal
amount of indebtedness outstanding under the term facility was $1.4 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

                                        5
<PAGE>   7

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 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, 2001

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           -- Fourth Amendment to Amended and Restated Letter Agreement
                            Between the Company and The Chase Manhattan Bank
          10.2           -- Revolving Promissory Note Between the Company and The
                            Chase Manhattan Bank
          10.3           -- Addendum to Lease Agreement by and Between the Company
                            and Robledo Investments, Ltd. dba Judson Plaza
</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, 2001                        By        /s/  BEN HARPER
                                            ------------------------------------
                                                  Ben Harper, Senior Vice
                                                     President-Finance
                                                 (Chief Accounting Officer)

Date August 13, 2001                        By      /s/  HAROLD FRIEDMAN
                                            ------------------------------------
                                              Harold Friedman, Vice Chairman of
                                                         the Board

                                        8
<PAGE>   10

                               INDEX TO EXHIBITS

<Table>
<Caption>
        EXHIBITS                                 DESCRIPTION
        --------                                 -----------
<C>                      <S>
         10.1            -- Fourth Amendment to Amended and Restated Letter Agreement
                            Between the Company and The Chase Manhattan Bank
         10.2            -- Revolving Promissory Note Between the Company and The
                            Chase Manhattan Bank
         10.3            -- Addendum to Lease Agreement by and Between the Company
                            and Robledo Investments, Ltd. dba Judson Plaza
</Table>