This story has been updated.
Paul's national political director John Yob accused Rubio (Fla.) deputy campaign manager Rich Beeson of hitting him.
"Last night I went to a bar on Mackinac Island for the GOP Mackinac Conference," Yob wrote on Facebook. "I ran into a guy named Rich Beeson, who frankly I didn't even know who it was at first because he isn't relevant in our political world. Anyway, he is Marco Rubio's national campaign manager [sic]. He literally physically assaulted me by punching me in the face."
Yob said the incident was captured "on video, from multiple angles."
Beeson did not immediately respond to a request for comment. Rubio spokesman Alex Conant said: "We're aware of the media reports and seeking more information about what happened."
Yob did not respond to an e-mail seeking a more detailed explanation of what happened.
Rand Paul's presidential campaign, which had promoted the 2014 hiring of Yob as a major coup, declined to comment on the alleged punch-up. Sources close to the campaign suggested that the disagreement was purely personality-based.
Yob did not say which bar he was at in his post. But West Michigan Politics blogger Brandon Hall, who wrote that he witnessed the confrontation, said it took place at Horn’s, where "police were summoned" by employees after the "fight dispersed."
Paul is scheduled to speak at the Mackinac Republican Leadership Conference on Saturday evening. Rubio is not scheduled to speak, though he has dispatched supporters to stump on his behalf.
Mackinac Island Police Chief Brett Riccinto told The Washington Post that no one was arrested or taken into custody, nor was medical attention administered.
"By no means was this a brawl," he said. "It was an incident."
Yob filed a complaint with the authorities claiming he was assaulted, which is being reviewed by a prosecutor.
Update, 2:25 p.m.: On Thursday afternoon, Yob pointed reporters to a Facebook post recently added by a GOP staffer:
David Weigel contributed to this story.