<PAGE>   1
 
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549
 
   
                                AMENDMENT NO. 1
    
   
                                       TO
    
 
                                   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, 1998
 
[ ] Transition Report Pursuant to Section 13 or 15(d) of the Securities Exchange
Act of 1934
 
                          COMMISSION FILE NO. 0-14836
 
                             METAL MANAGEMENT, INC.
             (Exact name of Registrant as specified in its charter)
 
<TABLE>
<S>                                      <C>
               DELAWARE                                94-2835068
     (State or other jurisdiction                   (I.R.S. Employer
   of incorporation or organization)             Identification Number)
</TABLE>
 
                        500 N. DEARBORN ST., SUITE 405,
                               CHICAGO, IL 60610
          (Address of principal executive offices including zip code)
 
       Registrant's telephone number, including area code: (312) 645-0700
 
     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 (or for such shorter period that the
Registrant was required to file such reports), and (2) has been subject to such
filing requirements for the past 90 days.      Yes [X]           No [ ]
 
     As of August 7, 1998, the Registrant had 39,099,812 shares of Common Stock
outstanding.
<PAGE>   2
 
                          PART II -- OTHER INFORMATION
 
   
ITEM 1.
    
 
   
     This Amendment No. 1 to Form 10-Q filed with respect to the Company's
fiscal quarter ended June 30, 1998 is being filed to include Exhibit 11.1
"Computation of Net Income (Loss) Per Share" which was inadvertently omitted
from the submission made by the Company on August 14, 1998.
    
 
ITEM 6: EXHIBITS AND REPORTS ON FORM 8-K
 
     (a) Exhibits
 
          See Exhibit Index
 
     (b) Reports on Form 8-K
 
          The following reports on Form 8-K were filed during the quarter ended
     June 30, 1998:
 
             (1) Form 8-K dated March 31, 1998, filed April 15, 1998 (describing
        the Company's Senior Credit Facility).
 
             (2) Form 8-K dated May 1, 1998, filed May 1, 1998 (relating to the
        acquisition of Aerospace Metals, Inc. and its consolidated subsidiaries
        and including historical and pro forma financial statements).
 
             (3) Form 8-K dated May 1, 1998, filed May 1, 1998 (describing
        certain risk factors related to an investment in the Company's
        securities).
 
   
             (4) Form 8-K dated May 13, 1998, filed May 22, 1998 (describing the
        Company's issuance of $180 million of Senior Subordinated Notes).
    
 
                                        1
<PAGE>   3
 
                                   SIGNATURES
 
     Pursuant to the requirements of Section 13 or 15(d) 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.
 
                                          METAL MANAGEMENT, INC.
 
                                          By:     /s/ GERARD M. JACOBS
 
                                            ------------------------------------
                                            Gerard M. Jacobs
                                            Director and
                                            Chief Executive Officer
 
                                          By:   /s/ T. BENJAMIN JENNINGS
 
                                            ------------------------------------
                                            T. Benjamin Jennings
                                            Director, Chairman of the Board
                                            and Chief Development Officer
 
                                          By:      /s/ ROBERT C. LARRY
 
                                            ------------------------------------
                                            Robert C. Larry
   
                                            Vice President of Finance,
                                              Treasurer,
    
   
                                            Chief Financial Officer and
                                              Assistant Secretary
    
 
   
                                          Date: August 19, 1998
    
 
                                        2
<PAGE>   4
 
                             METAL MANAGEMENT, INC.
 
                                 EXHIBIT INDEX
 
   
<TABLE>
<CAPTION>
         NUMBER AND DESCRIPTION OF EXHIBIT
         ---------------------------------
<C>      <S>
11.1     Computation of net income (loss) per share.
</TABLE>
    
 
                                        3