The Chicago Tribune's K.C. Johnson first reported Portis was expected to miss at least a month.
Portis suffered the injury during the fourth quarter of Wednesday night's 112-110 win over the Charlotte Hornets.
Prior to hitting the shelf, the fourth-year forward averaged 10.5 points, 10.0 rebounds and 1.0 blocks a night over the Bulls' first four games.
The Bulls are already without power forward Lauri Markkanen, who continues to nurse a right elbow sprain.
Until Portis or Markkanen return, Jabari Parker figures to be thrust into a prominent role at the 4 as head coach Fred Hoiberg scrambles for a stopgap solution in his suddenly decimated frontcourt.