SACRAMENTO, Calif.—California would become the first state to contract with generic-drug manufacturers to make prescription medicines to sell to residents, under a plan proposed by Gov. Gavin Newsom that aims to control rising health costs.

Mr. Newsom, a Democrat, said it will be part of his new budget proposal. Few details were provided about how the plan would work, what kind of drugs it would produce, how much it would cost to enact or how much it might save the state—things that are likely to be studied in more depth as...