Portis suffered the injury Wednesday in the Bulls' 112-110 win over the Charlotte Hornets -- Chicago's first win of the season -- when he collided with Hornets guard Tony Parker. Portis left the game immediately and did not return.
The 23-year-old power forward has averaged 10.5 points and 10.0 rebounds in the early going for the Bulls.
He joins a lengthy list of injured players for the Bulls: guard Kris Dunn is expected to be out four to six weeks with an MCL sprain; forward Lauri Markkanen, out with an elbow sprain, isn't expected back until November; and guard Denzel Valentine, who has an ankle injury, is sidelined for another couple of weeks.
After the Bulls' home game against Golden State next Monday, Chicago can apply for a hardship exception rule because Portis, Markkanen, Valentine and Dunn will have missed three games and are deemed to be out for the next two weeks. The NBA could grant the Bulls an extra roster spot.
In related Bulls news, the team has elected not to stretch Omer Asik, leagues sources told ESPN's Malika Andrews. As a result, Chicago will have a $3 million cap hit next season.