Beginning in April 2018, the US government will start mailing new Medicare cards to all people with Medicare in phases by geographic location. This will take a year to accomplish. The new cards will not include Social Security Numbers (SSN) but will include a new Medicare Beneficiary Identifier (MBI). Be on the look-out for your new card in the mail. And beware of scammers calling you now to try to get you to pay for a new card or trying to confirm your SSN.
To read more about what the new Medicare card, see this article on the CMS website.
To read an alert about the scams related to the new Medicare card, see this article.