Penny Marshall, the nasal-voiced co-star of the slapstick sitcom “Laverne & Shirley” and later the chronically self-deprecating director of hit films like “Big” and “A League of Their Own,” died on Monday at her home in Los Angeles. She was 75.

Her publicist, Michelle Bega, said the cause was complications of diabetes. Ms. Marshall had in recent years been treated for lung cancer, discovered in 2009, and a brain tumor. She announced in 2013 that the cancer was in remission.

Ms. Marshall became the first woman to direct a feature film that grossed more than $100 million when she made “Big” (1988). That movie, a comedy about a 12-year-old boy who magically turns into an adult (Tom Hanks) and then has to navigate the grown-up world, was as popular with critics as it was with audiences.

[An appraisal of Penny Marshall as Laverne.]

The Washington Post said it had “the zip and exuberance of a classic romantic comedy.” The Los Angeles Times described it as “a refreshingly grown-up comedy” directed “with verve and impeccable judgment.” Mr. Hanks received his first Oscar nomination for his performance.