The trouble started when the two fighters squared off in a photo op on a temporary stage in the lobby of the MGM Grand.
The taller Jones touched foreheads with Cormier, who shoved him backwards. Jones came right back at Cormier, with a pair of UFC employees shoved aside as they tried to intervene.
Both fights tumbled off the low stage, whose backdrop was ripped down, and landed in a pile of bodies before they were eventually pulled apart.
"I won't let another man get in my face and put his forehead against mine. I will react every time," Cormier tweeted later.
"Lol those baby punches from the bottom," Jones said by Twitter. "I really hope you have more prepared than that for when I take you down again."
No one was injured in the incident, according to the UFC.
UFC president Dana White normally MCs such events but missed this one.
"The first day of my vacation and this happens," the UFC boss said via Twitter, including a video of the scuffle.
The two fighters are slated to meet in the cage for real on Sept. 27. The two have made no secret of their dislike for each other, a sentiment that will undoubtedly help sell the fight.
Monday's brawl won't hurt either, although the UFC said the fighters would pay a price.
"This is certainly not a proud moment for the UFC organization," UFC chief legal officer Kirk Hendrick said in a statement. "We expect more from our athletes, especially these two gentlemen, who are very well-trained and highly educated professionals. Their actions were clearly a violation of the UFC’s code of conduct."
The UFC said the Nevada State Athletic Commission had requested a video copy of the incident.
"We are going to reserve our right to penalize both fighters after the commission has made a decision," Hendrick said. "We expect more from our athletes and we are prepared to levy sanctions to reinforce the appropriate behaviour."
"There are going to be ramifications," he added. "Whether you're the champion, or this is your first fight in the UFC, there are going to be ramifications from the UFC for these actions."