The altercation took place in Toronto during the Clippers' road trip. Griffin and the equipment staffer reportedly got into an argument, leading Griffin to hit the staffer inside the restaurant before following him outside and hitting him again.
The staffer's face was injured as a result of the attack, and he was treated at a nearby hospital.
Griffin and the staffer have been sent home for the remainder of the trip.
The 6-foot-10 power forward was already out with a torn quadriceps, and has missed Los Angeles' last 14 contests.
The 26-year-old was playing at an All-Star level prior to his injury, averaging 23.2 points, 8.7 rebounds, and five assists, while shooting 50.8 percent from the floor in 30 contests.
Luc Richard Mbah a Moute has struggled in his role as the Clippers' replacement starter, averaging just three points and 2.4 rebounds in 15.4 minutes.