Beshear later said it was too early to determine if the sites will be able to open Friday.
Wednesday marked the 15th straight day Kentucky has reported more than 30 virus-related deaths.
State health officials on Saturday reported 46 more deaths in which the coronavirus was a contributing factor, alongside 2,649 new cases of the respiratory virus.
Beshear on Monday said that 2,130 of the state's total deaths are attributed to the state's long-term care facilities.
The positivity rate hit its lowest point since Jan. 2 on Friday.
As of Saturday, 1,602 Kentuckians were hospitalized with COVID-19, the governor said, while 410 were being treated for the virus in intensive care units.
As of Friday, 1,644 Kentuckians were hospitalized with COVID-19, the governor said.
Wednesday's single-day death toll was the third-highest since the pandemic began.
As of Sunday, 1,713 Kentuckians were hospitalized with COVID-19, Gov. Andy Beshear said.
As of Saturday afternoon, 1,752 Kentuckians were hospitalized with COVID-19, according to Kentucky Public Health.