Dettman estimated it could take weeks to months to repair the damage. The expense could run into hundreds of thousands of dollars, depending on the extent of any structural damage, he said.
Lancaster said information was still being gathered about what exactly happened, but it appeared to be the first problem of its kind at the property.
Bowling Green sits in the midst of the state's largest karst region — the Western Pennyroyal area, where many of Kentucky's longest and deepest caves run underground. A karst region displays distinctive surface features, including sinkholes.
Sinkholes are common in the area, but this one was unique, Dettman said.
"One, it's full of Corvettes, and two that it was inside a structure," he said.
Geologists were still trying to determine what caused the sinkhole to open up.
Some of the foundation beneath the dome's main tower appeared to have been undermined, Dettman said, but "the primary foundation system around the perimeter of the structure hasn't been undermined."
Jason Polk, a geography and geology professor at Western Kentucky University, called it an isolated event, and said there was no indication that the sinkhole could spread.
"It's been stable," he said. "We haven't seen any other activity or movement since this morning."
Strode said it appeared at least two of the Corvettes could be saved, but museum officials were still trying to determine the extent of the damage and the value of the eight cars. He didn't know how soon the cars could be recovered.
"Safety will be paramount, but we'll also want to move as fast and as appropriate as we can," he said.
The museum is set to host the 2014 Corvette Caravan in late August, a celebration marking the museum's 20th anniversary. Museum officials expect car clubs from all 50 states and beyond to converge on Bowling Green for the celebration.
The museum had already hired an engineering firm to oversee the repairs, Strode said.
"The Corvette Museum has overcome adversity before and we'll overcome it again," he said. "And we'll have something spectacular to show you back there in short order."
Bowling Green, Ky., is also the lone place where General Motors builds the iconic Corvette.
Associated Press writers Brett Barrouquere and Rebecca Yonker in Louisville contributed to this report.