No. Reporting a lost card will not prevent its misuse. If you have lost your Social Security card you can apply for a replacement, but Social Security takes no special action because it has been lost.

If you think someone else might be using your card or number, call the Social Security Administration’s toll-free number (1-800-772-1213; TTY, 1-800-325-0778) and ask Social Security to review your earnings records to ensure they are correct. Likewise, verify your earnings each time you get your annual Social Security Statement. For further information about protecting your card and yourself, see Identity Theft and Your Social Security Number (Publication No. 05-10064) and Your Social Security Number and Card (Publication No. 05-10002).
 
Generally, the only time you will need to show a Social Security card is to your employer when you start a job. Therefore, if you anticipate starting new employment, you should request a replacement card in advance. You can replace your card for free if it is lost or stolen. However, you are limited to three replacement cards in a year and 10 during your lifetime. Legal name changes and other exceptions do not count toward these limits. For example, changes in noncitizen status that require card updates may not count toward these limits. Also, you may not be affected by these limits if you can prove you need the card to prevent a significant hardship.

To get a replacement card:

• Complete an Application For A Social Security Card (Form SS-5); and
• Show documents proving:
  • U.S. citizenship (or immigration status and work eligibility); and
  • Identity.
• Take (or mail) your completed application and documents to your local Social Security office.

For details about evidence requirements, see Documents You Need for a Social Security Card.

Keep your Social Security card in a safe place with your other important papers. Do not carry it with you.
The Federal Trade Commission also makes available on its web site the publication: "Take Charge: Fighting Back Against Identity Theft."  

If you think you might be a victim of identity theft, see "What do I do if someone else is using my Social Security number?