The death toll was last updated to 25 on Saturday.
"In more tough news for the commonwealth this morning, our death toll has risen to 26 lost – and that number will increase. There is widespread damage with many families displaced and more rain expected throughout the next day," Beshear tweeted.
US President Joe Biden declared a "major disaster" in Kentucky on Friday and approved federal funding for the state suffering from floods caused by heavy rains.
Earlier on Saturday, the Kentucky governor said that he total damage caused by powerful flood in the US state could reach hundreds of millions of dollars.
"I can't imagine that it's not going to be in the tens if not the hundreds of millions of dollars," Beshear told reporters.
On Thursday, Beshear appealed to US President Joe Biden, asking for federal aid due to the flooding caused by heavy rains. A state of emergency has been declared in Kentucky, with neighboring states of West Virginia and Tennessee sending their National Guard members to help.