Tillie suffered the injury in Thursday's victory over visiting San Francisco.
"We feel terrible for Killian," head coach Mark Few said in a statement. "He is an incredible teammate and an absolute joy to coach. Killian is a tough kid. We are hopeful treatment will go well and get him back for the postseason."
Tillie, a 6-foot-10 junior from France, missed the first 15 games of the season with an ankle injury and was still working his way back into the lineup. He was averaging 6.0 points and 4.2 rebounds in nine games this season but was one of the best players in the West Coast Conference last season.
When he was fully healthy a year ago, Tillie put up 12.9 points and 5.9 rebounds, while shooting 47.9 percent from 3-point range and establishing himself as one of the more versatile defensive players in the country.
With Tillie out, Gonzaga's frontcourt depth behind Rui Hachimura and Brandon Clarke will fall to senior Jeremy Jones and freshman Filip Petrusev, whose role has diminished considerably since Tillie returned to the fold.
The No. 4 Bulldogs (23-2, 10-0 WCC) beat Saint Mary's on Saturday night, 94-46.