By late Saturday afternoon, parts of southwestern Indiana had already experienced between 4 and 10 inches of rainfall, and more precipitation was expected, the agency reported.
The governor's office warned that Kentucky could see up to 7 inches of rain through Saturday evening, urging residents to remain vigilant.
Greg Eans/The Messenger-Inquirer via AP
He said on social media that three people had died in Madison County and one in Jackson County due to flooding.
"This is a serious flooding event, where teams have already had to conduct multiple water rescues from vehicles and homes across the commonwealth," he said in a statement. "As more heavy rain continues through late tonight, we need folks to remain alert and to avoid driving, especially after dark when there is limited visibility."
Beshear said there were "significant roads underwater" in Madison County, with search and rescue teams sent to that region. He also said at least 12 state roads were "out of commission" because they were flooded.
In northwestern Kentucky, just outside Louisville, Bullitt County emergency management officials asked residents of a rural road to evacuate as a precaution after a landslide at a dam embankment. The dam was holding and there was no indication of imminent failure, they said.
The area saw about 3 inches of rain in the past two days, according to the National Weather Service.