Washington coaches had to restrain Dime, who walked up to the student before slapping him after the halftime buzzer sounded.
"I was caught up in the emotion of the game and allowed my frustrations to influence my behavior," Dime said in a statement released by the school on Friday. "I made a very poor decision, and did not represent my team, my University and my family the way I want to.
"I am glad I had the chance to apologize in person to the students involved in the altercation, and I am prepared to accept the full consequences of my actions. I look forward to putting this incident behind me and moving forward."
The student who was slapped told the Tacoma News after the game that "everything's been made right."
Dime, who is from Dakar, Senegal, was sitting out his ninth consecutive game -- a 81-66 loss to the Buffs -- with a broken right pinkie.
"Malik's actions were inconsistent with his typical behavior," Washington coach Lorenzo Romar said in a statement. "They were absolutely unacceptable, and did not represent the values of our team and the sportsmanship spirit of our conference. We have spoken with him at length and expect this to be a valuable teaching moment. We do not expect this type of behavior to happen again."
Before getting hurt, Dime was averaging 5.5 points and 4.9 rebounds in 15 games. He still leads the Huskies with 39 blocked shots this season.
The Pac-12 said Friday that it was reviewing the incident.
The Associated Press contributed to this report.