No. The FDIC only insures deposits in deposit accounts at insured institutions. A safe deposit box is strictly a storage space provided by the bank.
IMPORTANT INSURANCE NOTICES:
• Contents Not FDIC Insured. The contents of your safe deposit box are NOT insured by the Federal Deposit Insurance Corporation (FDIC).
• (New Jersey) Important Notice: The contents of your vault, safe deposit box or storage receptacle are not protected against loss by the lessor unless specifically indicated in this notice, and for your protection you may wish to secure your own insurance for protection against loss with an insurance company of your own choice. You should keep a complete list and description of all your property stored in your vault, safe deposit box or storage receptacle and any available proof of ownership.
• (All states) Important Notice: (1) The contents of your safe deposit box may not be fully protected against loss under the insurance coverage maintained by the bank or safe deposit company. (2) For your protection, you may wish to secure your own insurance through an insurance company of your choice. (3) You should keep a complete list and description of all property stored in your safe deposit box, and any available proof of ownership.