The on-loan Liverpool player tore a medial knee ligament in training during Stoke's warm weather break in Dubai this week.
Morocco international Assaidi has impressed for the Potters this season, scoring four goals, including the winner against Chelsea in December.
He will stay with Stoke for treatment instead of returning to Liverpool, and manager Mark Hughes said: "It was our only negative from the trip away.
"Unfortunately he's torn his knee ligament and he's going to be out, so they tell me, for between four and six weeks.
"That's a real blow because he was looking really sharp and having a real effect on games for us. But given the medical cover that we have here and the quality of the staff, I'm sure he'll be back sooner rather than later."