Portis suffered the injury during the fourth quarter of Wednesday's 96-93 loss to the Brooklyn Nets, and he subsequently underwent an MRI.
The 23-year-old Portis has appeared in just nine games this season after previously missing time with a sprained MCL.
Portis is averaging 11.9 points and 8.0 rebounds per game primarily off the bench, but he has struggled as a shooter this season, making just 41.3 percent of his shots from the field and 25.0 percent from downtown, both of which are career worsts.
The 2015 first-round pick out of Arkansas had a career year last season with averages of 13.2 points and 6.8 rebounds. He also shot 47.1 percent from the field and became a three-point shooting threat by making 35.9 percent of his attempts from long range.
Portis' absence will likely mean even more playing time for the young frontcourt duo of rookie Wendell Carter Jr. and second-year man Lauri Markkanen, who has appeared in nine games since returning from injury.
Also, Jabari Parker figures to find his way back into the rotation after having played just four minutes over the past four games combined.
Parker has been the subject of trade rumors, but he is the Bulls' second-leading scorer this season with 15.2 points per game and the team's leading rebounder among players who have appeared in at least 10 games with 6.9 per contest.
With even less depth to speak of in the frontcourt now that Portis is on the shelf, it may be difficult for the Bulls to improve upon their NBA-worst 7-25 record in the coming weeks.