Syracuse caught a break for their upcoming game against No. 25 Notre Dame.
"It's a moderate pull," Brey said before Monday's practice. "We can't count on him Thursday and he's not going to be ready Thursday."
Freshman guard Rex Pflueger will make his first career start in place of Jackson, who leads the Irish with 16.6 points and 5.0 assists per game.
Pflueger, a 6-foot-6, 198-pound guard, scored 11 points in ND's 76-49 victory over Boston College on Saturday.
The Irish are 14-5 overall, 5-2 in the ACC.