Beshear had said earlier Sunday that at least 1,000 people stranded by floods had to be rescued. President Donald Trump approved Kentucky's request for a disaster declaration, authorizing the Federal Emergency Management Agency to coordinate relief efforts throughout the state.
Beshear said most of the deaths, including a mother and 7-year-old child, were caused by cars getting stuck in high water.
"So folks, stay off the roads right now and stay alive," he said.
Parts of Kentucky and Tennessee received up to 6 inches (15 centimeters) of rain, said Bob Oravec, a senior forecaster with the National Weather Service.