Her management at Roger Paul Inc told the BBC she died at her Los Angeles home on Thursday morning.
The agency said Ramsey had recently fallen ill, but did not give a cause of death.
Ramsey was adored by fans for her portrayal of the squeaky-voiced Officer Laverne Hooks in Police Academy.
She also had an illustrious career on Broadway, starring in the 1978 production Eubie!, a biographical musical about celebrated jazz pianist Eubie Blake.
"Her passion for performing and sharing her heart with the world was immense," Roger Paul Inc said in a statement.
"Marion carried with her a kindness and permeating light that instantly filled a room upon her arrival.
"The dimming of her light is already felt by those who knew her well. We will miss her, and always love her."
Born in Philadelphia, Pennsylvania in 1947, Ramsey started her career in the theatre, appearing in both the original Broadway and subsequent touring productions of Hello, Dolly!
She was prolific on Broadway, co-starring in many shows, including Harold Prince's Grind with Ben Vereen, and Eubie! with Gregory and Maurice Hines.
Her agent said Ramsey was "particularly proud" about Broadway's Dreamgirls finally becoming a major motion picture in 2006, because she was one of the singers that the original Broadway show's producer, Tom Eyen, based the three main characters on.
Ramsey's career in TV and film career took off after she appeared as a guest on the hit sitcom The Jeffersons in 1976.
Following that, she was a regular on Cos, Bill Cosby's sketch show.
She starred in six Police Academy films in total, making her a familiar face to fans of the franchise.