If you get Social Security benefits you can change your address online at ssa.gov by answering a series of questions that must match the information Social Security has in their records.
Additionally, you can call 1-800-772-1213.
If you received a Social Security Statement with an incorrect address, this is probably due to the fact that those addresses came from the Internal Revenue Service, so you must make the correction with them, not Social Security.
You can call the IRS toll-free telephone number at 1-800-829-3676 and ask for Form 8822.
For more Medicare FAQs please visit:
How Do I Change My Address for my Medicare Plan?