Museum officials said they got a call at 5:44 am from their security company because the motion detectors had gone off.
"Upon arrival it was discovered that a sinkhole had collapsed within the museum," the museum said in a statement.
The Bowling Green fire department came to secure the area and estimated the size of the hole at 40 feet (12 meters) across and 25 to 30 feet (8 to 9 meters) deep.
Two of the lost Corvettes -- a 1993 ZR-1 Spyder and a 2009 ZR-1 Blue Devil -- were on loan from General Motors.