The cause was complications from diabetes.
The latter work was the first film to be directed by a woman and gross more than $100 million (which now equates to around £80 million) in the US.
A League of Their Own was eventually chosen for preservation in the United States National Film Registry by the Library of Congress as being "culturally, historically, or aesthetically significant".
Penny Marshall, left, came to fame on Laverne and Shirley.
She moved to Los Angeles in 1967 and chose to look up her brother Garry, who, because of a 10-year age difference, se barely knew.
"Our family is heartbroken over the passing of Penny Marshall".
Marshall made the enormously charming and much loved The Preacher's Wife with Denzel Washington, Whitney Houston and Courtney B. Vance.
Penny Marshall was famous as an actress first.
'Garry also encouraged her to play on the softball team, which he was passionate about, and Penny was the best hitter. A wonderful actress, producer and director. As an actress, her work on "Laverne & Shirley" broke ground featuring blue-collar women entertaining America in prime time. Her first real name recognition came with a recurring part as a put upon secretary "nobody" ever called attractive on "The Odd Couple". Though her acting career waned in later years, she continued to pop up on television, often playing off her raspy voice and gruff demeanor on shows like Frasier, The Game and Portlandia.
Penny Marshall was a sweet woman. I had a good run, though, way more than my mother thought I would do.
Her recurring role on "Happy Days" as Laverne DeFazio led to the Garry Marshall-produced spinoff "Laverne & Shirley", which aired on ABC from 1976 to 1983 and was one of the most popular shows of the era. "We worked in a brewery".
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The 1990 drama, starring Robert De Niro and Robin Williams, saw Marshall become only the second woman to be nominated for the best director gong at the Academy Awards.
Marshall died "peacefully" in her California home on Monday.
The movie failed, but it opened the door to the film world, which paid off with "Big", the whimsical comedy-fantasy starring Tom Hanks. Hanks returned, alongside Geena Davis. (1989) and A League of Their Own.
She also directed A League Of Their Own, Jumpin' Jack Flash and Awakenings.
Penny was previously married to American actor and director Rob Reiner and he has joined her family in paying tribute. She had actually tried out for the role of Gloria on All In the Family, losing out to Sally Struthers for the role opposite Reiner.
Billy Crystal weighed in: 'Sad to hear of Penny Marshall's passing. a great comedienne a terrific director and a dear friend'.
The New York native was also a die-hard fan of the New York Knicks, seen often in the crowd at Madison Square Garden, and a collector of sports memorabilia.
In that memoir, she wrote that her "golden rules" were: "Try hard, play by the rules, help your friends, don't get too insane, and have fun". I was very fortunate to spend time with her.
A celebration of Marshall's life will be held at a later date to be announced, the family said.