Details were sketchy, but the first goal will be to target technology solutions to simplify the health system.
Cramer speculated whether Bezos could come up with a pricing model for prescription drugs, charging only a $50 fee on Amazon Prime subscriptions. Prime service currently grants perks for its users, including faster shipping and access to Amazon Video.
"Amazon Prime could make it so you pay a lot less for a lot of drugs," Cramer said on "Squawk on the Street."
Cramer cited Bezos' impact on other sectors, most notably retail.
"Think about what he did to every other business. How about that? Would you pay that to your premium because he's going to be the biggest buying group?" said Cramer, the host of CNBC's "Mad Money."
CNBC has previously reported Amazon was in talks with generic drugmakers about a potential entry into the pharmacy space.
In the announcement Tuesday, Bezos said: "The healthcare system is complex, and we enter into this challenge open-eyed about the degree of difficulty."