Kirk's comments were picked up on a live microphone during a Senate Appropriations Committee hearing.
"I've been joking with Lindsey," Kirk, R-Illinois, was heard saying. "Did you see that? He's going to have a rotating first lady. He's a bro with no ho."
In a chamber where senators practically trip over each other to maintain decorum despite bitter partisan differences, the vulgar comment was exceedingly unusual. Ho is slang for whore.
If elected president, Graham would become only the third unmarried president to move into the White House.
In an interview with the Daily Mail Online earlier this week, Graham poked fun at his bachelorhood, joking, "I've got a lot of friends. We'll have a rotating first lady."
Danielle Varallo, Kirk's press secretary, dismissed the remark, writing in a short statement to ABC News, "This was a joke between friends."
Thursday evening, Graham issued a brief statement reacting to the “joke” from Senator Kirk: “Sen. Kirk said he regrets the comments. I believe that is the appropriate response.”
Graham, a retired Air Force colonel who is viewed as one of the most hawkish lawmakers on Capitol Hill, entered the race for the Republican nomination for president on June 1.
White House press secretary Josh Earnest weighed in on the concept of a White House without a first lady – in the context of Graham’s comment that he’d have a “rotating first lady” if his campaign for president is successful.
“It's hard for me to imagine both a Graham White House and what a Graham White House would be without a first lady. But I would obviously defer to the senator to describe what that would be,” Earnest said.
Graham's campaign then fired back at the White House.
"Let’s imagine a White House without Barack Obama. A White House without a president who leads from behind, who doesn’t stand up for our allies, who doesn’t listen to his military commanders," spokeswoman Brittany Bramell noted. "Now let’s imagine a White House with a Commander-in-Chief ready on day one, a Commander-in-Chief like Lindsey Graham. A Graham White House would be respected by our allies and feared by our enemies. It’s not that hard to imagine a Graham White House, particularly with the nightmare Americans have been living through these last 6 years."
ABC News' Ali Weinberg and Ali Dukakis contributed to this report