McGregor turned himself into police on Thursday (Friday NZ Time) and was arrested and charged with three counts of assault and one count of criminal mischief after his role in the fracas that left UFC fighter Michael Chiesa in the hospital with a facial laceration, Reuters reported.
McGregor's bail as been set at $50,000.
White said the assault took place due to bad blood between McGregor and Nurmagomedov, a Russian fighter who was scheduled to fight for McGregor's vacated belt as the main event for Saturday's fight.
He appeared in court in NY on Friday (Saturday NZ time) and was freed on $50,000 bail, Reuters reported.
CNN could not reach McGregor's team for comment.
The judge also granted a request to allow to the Irish-born McGregor to travel outside the United States before his next court appearance on June 14.
White has said that the incident was the most "disgusting thing" that ever happened in UFC.
"No.no", White said on ESPN's Get Up! on Friday morning when asked if he would help McGregor. I don't think too serious. It was justified to him.
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White told ESPN that he texted with McGregor on Thursday after the incident.
Flyweight Ray Borg suffered multiple cornea abrasions in the wake of the McGregor attack and his fight against Brandon Moreno was also scratched. He said McGregor was "apologetic about the people he wasn't trying to hurt".
In a statement on Thursday, the UFC said McGregor, Lobov and more than a dozen others had "vandalised the vehicle", calling the disruption "completely unacceptable" and they are "working on the consequences that will follow".
McGregor was with fellow fighter Artem Lobov, who was due to fight featherweight Alex Caceres. The videos appear to show McGregor hurling large items at a bus that was boarded by rival fighter Khabib Nurmagomedov moments earlier. He had been brought out of a New York City police station in handcuffs after a backstage melee that forced the removal of three fights from UFC's biggest card of the year.
This Saturday's show was supposed to be headlined by Khabib Nurmagomedov's showdown against Max Holloway but the latter was deemed "unfit to fight".
McGregor has not fought in the UFC since November 2016 and at one point held two titles in simultaneously in the organization.