No injuries were reported when the ground caved in at the National Corvette Museum in the city of Bowling Green in the early hours of Wednesday.
Despite the hole, estimated to be 40ft (12m) wide and 30ft deep, parts of the museum remain open, said a spokeswoman.
Bowling Green is the only place where automobile-maker General Motors builds the Corvette sports car.
Two of the damaged cars - a 2009 ZR1 Blue Devil and a 1993 ZR-1 Spyder - were on loan to the museum from the company.
Six other cars owned by the museum were damaged by the sinkhole: a 1984 PPG Pace Car; a 1962 black Corvette; a 1993 Ruby Red 40th Anniversary Corvette; a 1992 White 1 Millionth Corvette; a 2001 Mallett Hammer Z06 Corvette; and a 2009 white 1.5 Millionth Corvette.