Surgery is not required to repair the injury, the Knicks said.
Prigioni suffered the fracture in the third quarter of the Knicks' 102-101 loss to the Wizards on Monday night. It appeared to be a noncontact injury. He exited with 9:49 left in the quarter and the Knicks trailing 57-42.
Prigioni's absence leaves the Knicks with a dire situation at point guard. Starter Raymond Felton is out with a strained left hamstring and could be sidelined at least two more weeks.
Coach Mike Woodson said shooting guard Iman Shumpert might fill in at point guard and that the Knicks might call up Chris Smith, J.R. Smith's brother, from the team's D-League affiliate, the Erie BayHawks.
New York also could look to make a trade to bolster the point guard position.
The Knicks, according to sources, balked at Toronto's demands to receive Felton, a first-round draft pick and either rookie Tim Hardaway Jr. or Shumpert in return for Lowry.
Talks had cooled off recently, but Prigioni's injury might force the Knicks, who now are 7-17, to rethink their stance on Lowry.
New York is optimistic that injured center Tyson Chandler will return to the court this week. Chandler has been out since Nov. 5 with a broken right leg. He is expected to participate in a full practice Tuesday.
The Associated Press contributed to this report.