<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, 1999

                                                              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  000-23213

                             YOUNG INNOVATIONS, INC.
             (Exact name of registrant as specified in its charter)

                  Missouri                                     43-1718931
(State or other jurisdiction of incorporation               (I.R.S. Employer
               or organization)                            Identification No.)


             13705 Shoreline Court East, Earth City, Missouri 63045
                    (Address of principal executive offices)
                                   (Zip Code)

                                 (314) 344-0010
              (Registrant's telephone number, including area code)


     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         
    -------    -------- 

Number of shares outstanding of the Registrant's Common Stock at April 30, 1999:
           6,508,296 shares of Common Stock, par value $.01 per share







                                       1
<PAGE>   2
                                     PART 1
                              FINANCIAL INFORMATION

Item 1. Financial Statements.


                             YOUNG INNOVATIONS, INC.

                           CONSOLIDATED BALANCE SHEETS
                        (IN THOUSANDS, EXCEPT SHARE DATA)

<TABLE>
<CAPTION>
                                                                             (UNAUDITED)
                                                                              MARCH 31      DECEMBER 31
                                                                                1999           1998
                                                                             -----------    -----------
<S>                                                                           <C>           <C>     
                                  ASSETS                                        
CURRENT ASSETS:                                                                        
  Cash and cash equivalents .............................................     $  5,247      $  4,337
  Trade accounts  receivable,  net of allowance for doubtful  accounts
     of $182 and $184, respectively .....................................        3,899         5,742

  Inventories ...........................................................        3,301         3,030

  Other current assets ..................................................        1,755         1,677
                                                                              --------      --------
     Total current assets ...............................................       14,202        14,786
                                                                              --------      --------
PROPERTY, PLANT AND EQUIPMENT ...........................................       11,862        11,713
                                                                              --------      --------
OTHER ASSETS ............................................................          277           282
                                                                              --------      --------
INTANGIBLE ASSETS .......................................................       27,777        27,963
                                                                              --------      --------
     Total assets .......................................................     $ 54,118      $ 54,744
                                                                              ========      ========

                  LIABILITIES AND STOCKHOLDERS' EQUITY
CURRENT LIABILITIES:
  Accounts payable and accrued liabilities ..............................     $  5,756      $  4,686
                                                                              --------      --------
     Total current liabilities ..........................................        5,756         4,686
                                                                              --------      --------
DEFERRED INCOME TAXES ...................................................        1,857         1,857
                                                                              --------      --------
STOCKHOLDERS' EQUITY:
  Common stock, voting, $.01 par value, 25,000,000 shares authorized,
     6,500,296 and 6,772,796 shares issued and outstanding in 1999 and
     1998, respectively .................................................           68            68
  Additional paid-in capital ............................................       26,083        26,083
  Retained earnings .....................................................       23,919        22,359
  Common stock in treasury,  at cost,  312,414 and 39,914  shares in 1999
     and 1998, respectively..............................................       (3,565)         (309)
                                                                              --------      --------
     Total stockholders' equity .........................................       46,505        48,201
                                                                              --------      --------
     Total liabilities and stockholders' equity .........................     $ 54,118      $ 54,744
                                                                              ========      ========
</TABLE>




The accompanying notes are an integral part of these statements.






                                       2
<PAGE>   3

                             YOUNG INNOVATIONS, INC.
                        CONSOLIDATED STATEMENTS OF INCOME
                      (IN THOUSANDS, EXCEPT PER SHARE DATA)
                                   (UNAUDITED)
<TABLE>
<CAPTION>
                                                      THREE MONTHS ENDED
                                                           MARCH 31
                                                       1999       1998
                                                      ------     ------
<S>                                                   <C>        <C>   
NET SALES                                             $8,951     $7,167
COST OF GOODS SOLD                                     3,949      3,049
                                                      ------     ------
               Gross profit                            5,002      4,118
SELLING, GENERAL AND ADMINISTRATIVE
       EXPENSES                                        2,529      2,112
                                                      ------     ------
               Income from operations                  2,473      2,006
                                                      ------     ------
OTHER INCOME
       Other income                                       84        161
                                                      ------     ------
                                                          84        161
                                                      ------     ------
               Income before provision for income      2,557      2,167
               taxes
PROVISION FOR INCOME TAXES                               997        823
                                                      ------     ------
               Net income                             $1,560     $1,344
                                                      ======     ======

BASIC EARNINGS PER SHARE                              $ 0.23     $ 0.20
                                                      ======     ======

DILUTED EARNINGS PER SHARE                            $ 0.23     $ 0.20
                                                      ======     ======

BASIC WEIGHTED AVERAGE SHARES OUTSTANDING              6,755      6,731
                                                      ======     ======

DILUTED WEIGHTED AVERAGE SHARES
       OUTSTANDING                                     6,761      6,790
                                                      ======     ======
</TABLE>


The accompanying notes are an integral part of these statements.




                                       3
<PAGE>   4
                             YOUNG INNOVATIONS, INC.
                      CONSOLIDATED STATEMENTS OF CASH FLOWS
                                 (IN THOUSANDS)
                                   (UNAUDITED)
<TABLE>
<CAPTION>
                                                                 THREE MONTHS ENDED
                                                                       MARCH 31
                                                                 1999          1998
                                                               --------      --------
<S>                                                            <C>           <C>     
CASH FLOWS FROM OPERATING ACTIVITIES:
  Net Income                                                   $  1,560      $  1,344
                                                               --------      --------
    Adjustments to reconcile net income to cash flows from
    Operating activities --
    Depreciation and amortization                                   513           383
    Loss on sale of property, plant and equipment                                 (22)
    Changes in assets and liabilities --
        Trade accounts receivable                                 1,843           528
        Inventories                                                (271)           77
        Other current assets                                        (78)          (39)
        Other assets                                                  5           534
        Accounts payable and accrued liabilities                  1,070          (225)
                                                               --------      --------
             Total adjustments                                    3,082         1,236
                                                               --------      --------

             Net cash flows from operating activities             4,642         2,580
                                                               --------      --------

CASH FLOWS FROM INVESTING ACTIVITIES:
   Payments for acquisitions, net of cash acquired                            (13,584)
   Purchases of property, plant and equipment                      (476)         (227)
   Proceeds from sale of property, plant and equipment                             13
   Proceeds from sale of marketable securities                                    100
                                                               --------      --------
             Net cash flows from investing activities              (476)      (13,698)
                                                               --------      --------

CASH FLOWS FROM FINANCING ACTIVITIES:
   Equity issuance costs                                                          (47)
   Purchases of treasury stock                                   (3,256)
                                                               --------      --------
           Net cash flows from financing activities              (3,256)          (47)
                                                               --------      --------

NET INCREASE (DECREASE) IN CASH AND CASH EQUIVALENTS                910       (11,165)
CASH AND CASH EQUIVALENTS, beginning of period                    4,337        12,761
                                                               --------      --------
CASH AND CASH EQUIVALENTS, end of period                       $  5,247      $  1,596
                                                               ========      ========
</TABLE>

The accompanying notes are an integral part of these statements.






                                       4
<PAGE>   5
                             YOUNG INNOVATIONS, INC.
              NOTES TO UNAUDITED CONSOLIDATED FINANCIAL STATEMENTS
                                 MARCH 31, 1999
                    (DOLLARS IN THOUSANDS, EXCEPT SHARE DATA)


1.   DESCRIPTION OF BUSINESS:

     Young Innovations, Inc. and its subsidiaries (the Company) develop,
manufacture and market supplies and equipment used by dentists and dental
hygienists. The Company's product offering includes disposable and metal prophy
angles, cups, brushes, panoramic x-ray machines and infection control products.
The Company's manufacturing facilities are located in Missouri, California,
Indiana and Texas. Export sales were less than 10% of total net sales for 1998,
1997 and 1996. Since the acquisition of Panoramic, the Company has two operating
segments: preventative and diagnostic. The preventative segment produces
disposable and metal prophy products. The diagnostic segment sells and rents
dental x-ray equipment. Management believes it is appropriate to aggregate these
operating segments into a single reportable segment. This aggregation is due to
similarities in economic characteristics, customers, the nature of the products
and the nature of the production processes.

2.   SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES:

PRINCIPLES OF CONSOLIDATION

     The consolidated financial statements include the accounts of Young
Innovations, Inc. formed in July 1995 and its direct and indirect wholly owned
subsidiaries, Young Dental Manufacturing Company (Young Dental), The Lorvic
Corporation (Lorvic), Denticator International, Inc. (Denticator), Young
Acquisitions Company and Panoramic Rental Corp. (collectively, Panoramic).
Panoramic is included since its acquisition on February 27, 1998. All
significant intercompany accounts and transactions are eliminated in
consolidation.


2. ACQUISITIONS:

     On February 27, 1998, the Company acquired the assets and assumed certain
liabilities of Panoramic, an Indiana corporation. The Company paid $13,875 in
cash and issued $1,000 (62,500 shares) of common stock. The cash portion of the
purchase price was principally financed with the net proceeds remaining from the
Company's initial public offering. The acquisition was accounted for as a
purchase transaction. The purchase price was allocated based upon estimates of
fair value. The excess of purchase price over the estimated fair value of net
assets acquired (goodwill) was $10,445 and is being amortized over 40 years. The
results of operations for Panoramic are included in the consolidated financial
statements since February 27, 1998.

     The following unaudited pro forma information presents a summary of
consolidated results of operations of the Company and Panoramic as if the
acquisition had occurred at the beginning of 1998, with pro forma adjustments to
give effect to amortization of goodwill and certain other adjustments, together
with related income tax effects. The unaudited pro forma information does not
purport to be indicative of the results of operations had these transactions
been completed as of the assumed dates or which may be obtained in the future.


<TABLE>
<CAPTION>
                                                            QUARTER
                                                             ENDED
                                                            MARCH 31,
                                                              1998
                                                           -----------
                                                           (UNAUDITED)
<S>                                                         <C>      
        Net sales.......................................    $   8,591
        Net income......................................        1,362
        Basic and diluted earnings per share............          .20
</TABLE>



                                       5
<PAGE>   6


4.  INVENTORIES:

    Inventories consist of the following:
<TABLE>
<CAPTION>
                                                                             MARCH 31  DECEMBER 31
                                                                               1999        1998
                                                                             --------  -----------
<S>                                                                          <C>         <C>    
              Finished products......................................        $ 1,070     $ 1,011
              Work in process........................................          1,331       1,069
              Raw materials and supplies.............................            900         950
                                                                             -------     -------
                   Total inventories.................................        $ 3,301     $ 3,030
                                                                             =======     =======
</TABLE>

5.  COMMON STOCK:

    In March 1999, the Company authorized the repurchase of up to 300,000 shares
of its common stock. As of March 31, 1999, the Company had completed the
repurchase of 272,500 shares for $3,256.

6.  SUBSEQUENT EVENT:

    On April 2, 1999, the Company acquired Athena Technology, Inc.
("Athena/Champion"). Athena/Champion develops, manufactures and markets
handpieces, related components and supplies for the dental market. The purchase
price was approximately $4.9 million, including the assumption of approximately
$1 million in debt.



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

RESULTS OF OPERATIONS

THREE MONTHS ENDED MARCH 31, 1999 COMPARED TO THREE MONTHS ENDED MARCH 31, 1998

NET SALES
         Net sales increased $1.8 million, or 24.9%, to $9.0 million in the
first quarter of 1999 from $7.2 million in the first quarter of 1998. The
increase was primarily attributable to the inclusion of a full quarter of
Panoramic sales in the first quarter of 1999 as compared to a partial quarter in
1998. Panoramic was acquired February 27, 1998.

GROSS PROFIT
         Gross profit increased $884,000, or 21.5%, to $5.0 million in the first
quarter of 1999 from $4.1 million in the first quarter of 1998. Gross profit
benefited from the acquisition of Panoramic. Gross margin decreased to 55.9% of
net sales in 1999 from 57.5% in 1998. The Company's gross margin decreased
primarily as a result of the inclusion of Panoramic sales, which historically
have lower margins.

SELLING, GENERAL, AND ADMINISTRATIVE EXPENSES
         SG&A expenses increased $417,000, or 19.7%, to $2.5 million in the
first quarter of 1999 from $2.1 million in the first quarter of 1998. As a
percent of net sales, SG&A expenses decreased to 28.3% in 1999 from 29.5% in
1998. SG&A expenses increased primarily due to the addition of Panoramic.

INCOME FROM OPERATIONS
         Income from operations increased $467,000 or 23.3%, to $2.5 million in
the first quarter of 1999 from $2.0 million in the first quarter of 1998.

OTHER INCOME (EXPENSE)
         Other income (expense) decreased $77,000 to $84,000 in the first
quarter of 1999 from $161,000 in the first quarter of 1998. The decrease is
primarily due to lower interest income in 1999 as compared to 1998. A majority
of the 1998 interest income resulted from interest earned on the net proceeds
from the initial public offering prior to the acquisition of Panoramic.

                                       6
<PAGE>   7

PROVISION FOR INCOME TAXES
         Provision for income taxes increased $174,000 for the first quarter of
1999 to $997,000 from $823,000 in the first quarter of 1998.


LIQUIDITY AND CAPITAL RESOURCES

    On February 27, 1998, the Company acquired the net assets of Panoramic. The
Company paid approximately $13.9 million in cash plus $1.0 million (62,500
shares) of its common stock. The acquisition was principally financed with cash
remaining from the net proceeds of the Company's initial public offering.

    Historically, the Company has financed its operations primarily through cash
flow from operating activities and, to a lesser extent, through borrowings under
its credit facilities. Net cash flow from operating activities was $4.6 million
and $2.6 million for the first quarter of 1999 and 1998, respectively. Capital
expenditures for property, plant and equipment were $476,000 and $227,000 in the
first quarter of 1999 and 1998, respectively. Consistent with the Company's
historical capital expenditures, future capital expenditures are expected to
include injection molding equipment, panoramic X-ray machines for rental,
computer numeric controlled equipment and upgrades to production machinery and
to the Company's information systems. Management believes the Company has
adequate liquidity and capital resources to meet its needs on a short and
long-term basis.



Item 3. Quantitative and Qualitative Disclosures About Market Risk

Not required.


                                     PART II
                                OTHER INFORMATION


Item 6. Exhibits and Reports on Form 8-K

(a)  Exhibits.
     ---------
      Number       Description
     ---------     -----------

        27         Financial Data Schedule

(b)  Reports on Form 8-K.
     --------------------
     None

Signature
---------
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.

                                                     YOUNG INNOVATIONS, INC.

May 14, 1999                                         /s/George E. Richmond
------------                                         -------------------------  
Date                                                 George E. Richmond
                                                     Chief Executive Officer








                                       7