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.