The red-shirted attacker – believed to be a UFC fighter – leapt into the cage and threw several punches at McGregor before security intervened.
Nurmagomedov had earlier jumped out of the octagon himself to wage an attack on Dillon Danis, one of McGregor’s training partners.
Dana White later told Fox Sports that three members of Nurmagomedov’s team were arrested.
He told ESPN it was “a very bad night” for the UFC and said: “Khabib diving over [the cage] was ridiculous.
“You know, you just won a great fight, you fought brilliantly, you’re about to get the belt on and people are going to respect the fact that you fought well and you won the fight, and instead you dive over the cage and start this huge melee with Conor’s corner.”
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White refused to give the champion his belt and revealed Nurmagomedov’s winnings were also withheld.
The Nevada State Athletic Commission had paid McGregor after reviewing footage of the brawl.
Nurmagomedov apologised at the post-fight press conference and said: “I want to say sorry to the Nevada State Athletic Commission.
“This is not my best side. He talked about my religion, my country, my father. He came to Brooklyn, he broke a bus and nearly killed two people. So why do people still talk about me jumping over the cage? I have shown respect.
“I told you guys: his whole team and him, they are tap machines. Today he tapped. (I am) Undisputed and undefeated.
“This is a respectful sport. This is not a trash-talking sport. I want to change this game. You cannot talk about religions and nations.
“This for me is very important. Thank you for waiting for me. I know my father is gonna smash me when I go home. Nevada: sorry. Vegas: sorry.
“He took a picture with Putin. But Putin just called me and told me he is proud of me. And he said congratulations.”
Khabib’s attack on Danis could be a case for the Las Vegas police, who could decide to prosecute the 30-year-old.
He will also receive a fine from the Nevada State Athletic Commission for leaving the Octagon post-fight, despite his apology to the body.
Khabib could also see his MMA license revoked.
However, White has already confirmed that the Russian will not receive his purse for the fight, while McGregor has already been paid.
Khabib wasn’t given his belt in the ring after the fight as UFC chiefs feared another fight would break out.