McConnell has been out of the public eye since being hospitalized on June 14, and has only released statements and still photos in the months after.
Beshear told reporters Wednesday the lack of direct communication with colleagues and constituents demands more than the explanations they've received so far.
"If he is not there on Monday, he owes an explanation to the American people (and) to the people of Kentucky," the governor said.
Addressing questions about what actions his office can take, Beshear put the onus on Senate leadership.
"For some of those online that wonder why you can't just storm into wherever he is, he is in D.C, which means that John Thune... has a responsibility to check on him and report to the American people. He will not do it. This is the leader of the Senate," Beshear said.
The governor called Thune's response "shameful."
While several Kentucky leaders on Capitol Hill have said they expect McConnell to return this month, the senator's office says there are no scheduling announcements as of yet.
Republicans are hoping McConnell will be back, as lawmakers need his help to move a large package of nutrition, agricultural, and food policy known as the Farm Bill.