Like many huge establishments in Cuba, their supermarkets are owned and operated by the government. But the government isn’t doing a very good job, at least by US standards. If you step into a Cuban supermarket, odds are the shelves are going to be completely void of anything.
Most of the time, you’ll find what you’re looking for in private-owned roadside shops. The prices are usually fairer than supermarkets, and you’ll most likely walk away with exactly what you needed. If you’ve seen any of the tons of zombie movies where the protagonist enters a supermarket and sees nothing on the shelves, that’s what it’s like in Cuba.