A women was spotted driving the car at speed near the river, damaging several cars before crashing through a barrier into the water.
The incident happened on Lapwing Road, next to the Braehead shopping centre in Renfrew, at about 13:20.
Divers were deployed at the scene to rescue any occupants.
Police have cordoned off Clyde View Park with the public asked to vacate the area where emergency service teams are working.
In a statement Police Scotland said: “A full search of the water surface has been conducted by divers from Police Scotland’s Marine Unit and a woman has now been recovered from the vehicle.
“She was the only person in the car.
“A post mortem examination will take place in due course to establish the exact cause of death.
“The car remains in the water at this time and efforts are ongoing to remove it.”
Enquiries are continuing to establish the exact circumstances of how the vehicle came to enter the River Clyde, with crash scene examiners conducting an investigation at the location.