Rove, the mastermind behind George W. Bush's two presidential election victories, appeared at a conference last week, where he discussed a 2012 incident that sent the then-secretary of state to the hospital, according to the New York Post's Page Six gossip column.
"Thirty days in the hospital?" asked Rove, a Fox News Channel contributor, according to the report. "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."
Clinton, who's seriously considering a second bid for the White House, suffered a blood clot in December 2012, after falling. After first going to the hospital for testing, Clinton later was admitted for a three-day stay at a hospital in New York.
The incident prevented her from testifying before Congress about the deadly 2012 terror attack on the American diplomatic compound in Benghazi, Libya, raising questions from some Republicans. She eventually appeared before lawmakers in January 2013.
Should Clinton, 66, decide to seek the presidency, her health likely would be raised in the same context as any other candidate.
Democrats and others were quick to slam Rove. The Democratic National Committee put out a statement saying, "It appears Karl Rove's medical diagnoses are about as solid as his election night prognostications."
The statement refers to Rove's prediction that Mitt Romney would win the 2012 presidential election.
Clinton spokesman Nick Merrill said "Karl Rove has deceived the country for years, but there are no words for this level of lying."
As for Clinton's health, Merrill added, "She is 100%. Period."
Former president weighs in
On Wednesday, former President Bill Clinton said he was "sort of dumbfounded" by the comments.
"Look, she works out every week, she is strong, she's doing great. As far as I can tell she's in better shape than I am. She certainly seems to have more stamina now," he said.
Clinton also joked about Rove.
"I got to give him credit, you know, that embodies that old saying that consistency is the hobgoblin of little minds. First they said she faked her concussion. And now they say she's auditioning for a part on the Walking Dead," he said.
Rove defended his comments on Tuesday on Fox News Channel, saying that it's legitimate to ask about a potential presidential candidate's health.
"No, no. I didn't say she had brain damage, she had a serious health episode and my point was that I think it was from the 7th of December in 2012 through the 7th of January of 2013, she underwent, first she had apparently a serious virus.
"They announced then on the 15th of December that she had at some period in the past week fallen. They didn't say when, they didn't say where. She was recovering at home. On the 30th of December she goes in and turns out to have had a blood clot. They won't say where.
"The next day they say it is between her skull and her brain behind her right ear. She is in the hospital for four days. She goes home, is back in the office on the 7th and testifies on the 25th wearing special glasses that allow her to deal with the double vision that this episode caused," Rove said
While she was hospitalized, Clinton's doctors said they were confident that she would make a full recovery.
Clinton has increasingly come under attack by Republicans as she seriously considers a presidential bid. If she decides to run, she would instantly become the overwhelming frontrunner for the Democratic nomination. At the same time, Clinton is keeping up a very demanding speaking schedule that includes lots of travel.
Stepped up attacks
While she mulls her decision, the GOP and pro-Republican outside groups have stepped up their attacks on Clinton, on everything from the Benghazi incident to the 1990s Monica Lewinsky scandal.
Rove said Clinton's health will be a factor if she runs.
"My point was that Hillary Clinton wants to run for president, but she would not be human if this didn't enter in as a consideration. My other point is this will be an issue in the 2016 race whether she likes it or not. Every presidential candidate is asked for their health records," Rove added Tuesday.
Following Rove's appearance on Fox News, Merrill released a new statement.
"From the moment this happened 17 months ago, the Right has politicized her health. First they accused her of faking it, now they've resorted to the other extreme -- and are flat out lying. Even this morning, Karl Rove is still all over the map and is continuing to get the facts wrong. But he doesn't care, because all he wants to do is inject the issue into the echo chamber, and he's succeeding. It's flagrant and thinly veiled," Merrill said.
The 2012 incident was not the first time Clinton dealt with blood clots.
She told the New York Daily News in 2007 that while campaigning for Sen. Chuck Schumer in 1998 she suffered a large blood clot behind her right knee and had to be rushed to Bethesda Naval Hospital.
Clinton also fell and fractured her right elbow as secretary of state in 2009 and was treated at George Washington University Hospital.
Age an issue in presidential elections
Rove pointed out that some Democrats in 2008 made Republican presidential nominee John McCain's age an issue during the campaign. The age attacks were not limited to outside groups, either. Then-Sen. Barack Obama said McCain had "lost his bearings" while pursuing the Republican nomination, a line that was seen as a subtle attack.
Age is often made a campaign issue. Bill Clinton's campaign portrayed incumbent George H.W. Bush as old and out of touch during the 1992 presidential race.
Then-President Ronald Reagan famously turned the issue on its head in 1984 by telling voters during a debate with challenger Walter Mondale that "I am not going to exploit, for political purposes, my opponent's youth and inexperience."