Rove came under fire last week when he suggested the former secretary of state -- who may or may not run for president in 2016 -- may have suffered brain damage after a concussion she suffered in a fall in December 2012.
"Thirty days in the hospital? And when she reappears, she's wearing glasses that are only for people who have traumatic brain injury? We need to know what's up with that," he said a conference near Los Angeles.
He later backtracked on his comments, saying "of course she doesn't have brain damage."
"I think that health and age is fair game," Priebus said in an appearance on NBC's Meet the Press.
Clinton will be 69 years old in 2016.