According to the gubmint, they are rolling out new Medicare cards on which the SSN is replaced with a newly assigned Medicare Beneficiary Identifier.
https://www.cms.gov/Medicare/New-Medicare-Card/index.html
"We've often heard from Congress, the General Accountability Office, people with Medicare, and advocacy groups that they want the SSN taken off Medicare cards."
I saw that...after the horse is out of the barn.