Dvalishvili called Nurmagomedov’s older brother, Umar, “spoiled” before beating him in a bantamweight title fight in 2025.
Umar Nurmagomedov is due to take on American Urijah Faber at Saturday’s event.
There was previously an altercation between the two camps before the RAF event in July.
UFC champion Islam Makhachev, who is a close friend and training partner of the Nurmagomedovs, suggested that incident led to Wednesday’s altercation.
“Why were you silent when Merab hit a Dagestani wrestler for nothing and hurt his honor?” Makhachev wrote.
“Merab started what happened today in his homeland by allowing himself to hit a guest and insulting his mother.”
Two-weight UFC champion Ilia Topuria, a friend of Dvalishvili, shared the footage of the incident on X and wrote: “Usman has reportedly been detained, along with the cowards who were with him.
“What a disgrace. A bunch of absolute cowards. I always thought you were a bunch of mediocre individuals. Now you’ve removed every last doubt.
“Honour, respect, and humility aren’t words you preach. They’re values you live by. And you’ve shown none of them.”
Nurmagomedov is a free agent after his last fight with the PFL and has been heavily linked with a switch to the UFC.
MMA fighters often compete in RAF events alongside their careers in bigger promotions, with the likes of Khamzat Chimaev, Arman Tsarukyan and Colby Covington all recently appearing in the promotion.