<PAGE>   1
                                  UNITED STATES
                       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 March 31, 1997
                                       OR
[ ] TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES
EXCHANGE ACT OF 1934

For the transition period from                      to


Commission file number   1-5542

                             THE DEXTER CORPORATION
             (Exact name of registrant as specified in its charter)

<TABLE>
<S>                                                 <C>
CONNECTICUT                                             06-0321410
(State or other jurisdiction of                      (I.R.S. Employer
incorporation or organization)                      Identification No.)

ONE ELM STREET, WINDSOR LOCKS, CONNECTICUT                    06096
(Address of principal executive offices)                   (Zip Code)
</TABLE>

(860) 292-7675
(Registrant's telephone number, including area code)

N/A
(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 (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

Indicate the number of shares outstanding of each of the issuer's classes of
common stock, as of the latest practicable date.

<TABLE>
<CAPTION>
       CLASS                                  Outstanding at April 30, 1997
--------------------------                    -----------------------------
<S>                                           <C>
COMMON STOCK, PAR VALUE $1                        23,032,526 SHARES
</TABLE>
<PAGE>   2
                                     PART I

                              FINANCIAL INFORMATION

Item 1 -     Financial Statements

             Reference is made to the following consolidated financial
             statements which are incorporated herein by reference:

             (a)  Exhibit 99a - Condensed Statement of Income for the three
                  months ended March 31, 1997 and 1996.

             (b)  Exhibit 99b - Condensed Statement of Financial Position as of
                  March 31, 1997, December 31, 1996, and March 31, 1996.

             (c)  Exhibit 99c - Condensed Statement of Cash Flows for the three
                  months ended March 31, 1997 and 1996.

             (d)  Exhibit 99d - Net Sales by Market for the three months ended
                  March 31, 1997 and 1996.

             (e)  Exhibit 99e - Notes to Consolidated Financial Statements.

             The unaudited financial data included herein as of March 31, 1997
             and 1996, and for the three-month periods then ended, have been
             reviewed by the registrant's independent public accountants,
             Coopers & Lybrand L.L.P., and their report is attached.


Item 2 -     Management's Discussion and Analysis of Financial
             Condition and Results of Operations

             The Company reported record first quarter earnings of $12.9
             million, or $.55 per share, compared with $11.1 million, or $.46
             per share, for the first quarter of 1996. Net income increased 15%
             while earnings per share improved 20% in the first quarter.

             Sales for the first quarter of 1997 were $272.3 million, a 2%
             decrease compared with sales of $277.2 million, in the first
             quarter of 1996. A 3% gain in unit volume was more than offset by a
             2% decrease due to net effect of acquisitions and divestitures, a
             2% unfavorable effect of currency exchange rates, and price
             decreases averaging 1%.

             Products with strong performance in the first quarter include
             aerospace adhesive materials, liquid encapsulant materials serving
             the electronics market, medical nonwoven material, and sales of
             products at Life Technologies, Inc. other than fetal bovine serum.
             Products with weaker performance include magnetic materials,
             beverage can coatings serving the international markets, and fetal
             bovine serum.

             Other income was $4.2 million for the first quarter of 1997, an
             increase of $2.0 million over the first quarter of 1996. This
             increase is primarily due to higher equity income from companies
             owned 50% or less, principally D & S Plastics International in
             addition to higher royalty income at Life Technologies, Inc.
<PAGE>   3
Item 2 -     Management's Discussion and Analysis of Financial
             Condition and Results of Operations, continued


             Consolidated gross margin of 35.6% of net sales in the first
             quarter of 1997 improved by 1.4 percentage points from 34.2% in the
             first quarter of 1996. This increase is primarily attributable to
             higher gross margins at Life Technologies, Inc., and the net
             favorable effect of lower raw material costs offset by lower
             selling prices at wholly owned Dexter businesses.

             Marketing and administrative costs and R&D expense increased in the
             first quarter of 1997 due to increased cost at Life Technologies,
             Inc.

             Effective April 1, 1997, the Company completed the divestiture of
             its 50% interest of D & S Plastics International, an equally owned
             joint venture between The Dexter Corporation and the Solvay Group
             to Solvay America, Inc. of Houston, Texas. D & S Plastics is the
             largest North American supplier of elastomer modified thermoplastic
             olefins (TPO) to the automotive industry and a recognized leader in
             TPO applications engineering.






























<PAGE>   4
                                     PART II

                                OTHER INFORMATION


Item 4 -    Submission of Matters to a Vote of Security Holders

            The annual meeting of the shareholders of the Company was held on
            April 24, 1997, where the following actions were taken:

      (a)   The re-election to the Board of Directors of Mr. Charles H. Curl,
            president of Curl & Associates; Peter G. Kelly, Esq., chairman of
            Updike, Kelly & Spellacy, P.C.; and Mr. Jean-Francois Saglio,
            president of the French National Institute for the Environment and
            president of ERSO.

            The votes for each director were as follows:

<TABLE>
<CAPTION>
            Director                        For                     Withheld
            --------                        ---                     --------
<S>                                      <C>                        <C>
            Charles H. Curl              18,859,072                 2,705,870
            Peter G. Kelly               18,762,561                 2,802,381
            Jean-Francois Saglio         19,184,828                 2,380,114
</TABLE>

            In addition, the following directors continue in office for the
            terms expiring as indicated: Mr. Robert M. Furek (1998), Mrs. Martha
            Clark Goss (1998), Mr. Edgar G. Hotard (1998), Glen L. Urban, Ph.D.
            (1998), Ms. Henrietta Holsman Fore (1999), Mr. Bernard M. Fox
            (1999), Mr. K. Grahame Walker (1999), and George M. Whitesides,
            Ph.D. (1999).


      (b)   The selection of Coopers & Lybrand L.L.P. as auditors of the Company
            for the year 1997 was ratified.

            The votes for selection of Coopers & Lybrand L.L.P. were as follows:

<TABLE>
<CAPTION>
                     For                 Against               Abstain
                     ---                 -------               -------
<S>                                      <C>                   <C>
                 21,502,368              22,429                40,145
</TABLE>


Item 6 -    Exhibits and Reports on Form 8-K

      (a)   Exhibit 15 of Part 1 - Letter to Securities and Exchange Commission
            re: Incorporation of Accountants' Report

            Exhibit 27 of Part 1 - Financial Data Schedule

            Exhibit 99 of Part 1 - First Quarter 1997 Financial Statements and
            Notes

      (b)   No reports on Form 8-K were filed during the quarter for which this
            report was filed.
<PAGE>   5

                                   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.



                                               THE DEXTER CORPORATION


Date    May 9, 1997                            /s/ Kathleen Burdett
     -----------------------------             --------------------------------
                                               Kathleen Burdett
                                               Vice President and
                                               Chief Financial Officer
                                               (Principal Financial Officer)





Date    May 9, 1997                            /s/ George Collin
     -----------------------------             --------------------------------
                                               George Collin
                                               Controller
                                               (Principal Accounting Officer)
<PAGE>   6
                                INDEX TO EXHIBITS







Exhibit No.

15         Letter to Securities and Exchange Commission re:  Incorporation of
           Accountants' Report

27         Financial Data Schedule

99         First Quarter 1997 Financial Statements and Notes