Griffin fractured the fourth metacarpal in his right hand while punching one of the team's equipment managers outside of a Toronto restaurant on Saturday.
According to the Orange County Register, the two had an argument inside the establishment, and once outside, Griffin hit the staff member multiple times.
The Clippers confirmed that Griffin was injured while throwing a punch but gave no additional details.
Griffin returned to Los Angeles on Monday for X-rays and had surgery on Tuesday, the team announced. He will be sidelined for four to six weeks.
"This conduct has no place in our organization and this incident does not represent who we are as a team," the Clippers said in a statement. "We are conducting a full investigation with assistance from the NBA. At the conclusion of the investigation, appropriate action will be taken."
Griffin issued an apology on Twitter later Tuesday.
"A situation among friends escalated and I regret the way I handled myself towards someone I care about," he wrote. "I want to apologize to the Clippers organization, my teammates and the fans for creating a distraction. I am working with the team on a resolution and getting back in the game as soon as possible."
Clippers coach Doc Rivers reacted to the incident with frustration.
"You don't want it to happen to anyone, and you obviously don't want it to happen during the season or even when the season is not going on," Rivers said. "This type of stuff shouldn't happen, but it did, and it's real life, and you have to deal with real life sometimes in our make-believe world."
The latest injury is unrelated to the leg injury that kept Griffin out the past four weeks.
Without Griffin in the lineup, the Clippers are 12-3 following a 91-89 victory Tuesday night at Indiana.