Griffin, who was already recovering from injury and expected to return soon, will be on the shelf for another four to six weeks after breaking a bone in his right hand during the fight in Toronto, according to an ESPN report.
Griffin apologized for the incident on Twitter, saying it was a "situation among friends" that got out of hand, and he was ashamed for how he behaved.
ESPN reported that Griffin had struck Matias Testi, who serves as the assistant equipment manager for the Clippers.
Griffin and Testi had apparently traded insults at a restaurant, prompting Griffin to strike Testi. Testi left and went outside, but Griffin came after him and struck him again, leaving injuries on Testi's face.
Griffin and Testi are reportedly good friends, and both were sent home after the incident. Clippers coach Doc Rivers told reporters that the incident was "frustrating." A statement from the team said the incident had "no place" within the organization. The NBA Players Association is investigating the incident.
The Clippers are currently in 4th place in the competitive Western Conference with a 29-16 record, behind the Oklahoma Thunder, San Antonio Spurs, and Golden State Warriors. They have gone 7-3 in their past 10 games.
Griffin, who is 26, was the first overall pick in the 2009 NBA draft out of Oklahoma. He has spent his entire career with the Los Angeles Clippers, and he has been elected to the NBA All-Star game five times.