Federal health regulators have proposed banning Theranos Inc. founder Elizabeth Holmes from the blood-testing business for at least two years after concluding that the company failed to fix what regulators have called major problems at its laboratory in California.

In a letter dated March 18, the Centers for Medicare and Medicaid Services said it plans to revoke the California lab’s federal license and prohibit its owners, including Ms. Holmes and Theranos’s president, Sunny Balwani, from owning or running any other lab for...