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."
Hughes, though, denied rumours that Robert Huth has suffered a setback in his recovery from knee surgery.
The key defender went under the knife at the end of November and it had initially been hoped he would only be missing for around three to four weeks.
Huth has made slow progress, but Hughes said: "He's doing very well.
"He's trained again with the group on Thursday. He's completed two full training sessions with the squad now. We're able to manage the injury and it seems to be reacting well to work so that's encouraging for him and for us.
"He's progressed quicker in the last couple of days when people have been saying that he's had a setback so I don't really know where that story's come from.
"He probably needs game time now. If we can get him playing then obviously that's the next step for him.
"We have games organised that he could play a part in so, as long as he's dealing with the training load that we're giving him, which he seems to be, then we'll look to get him game time next week and the week after."
Hughes also confirmed that goalkeeper Jack Butland is in talks with Leeds over a loan move.
The 20-year-old played four games for the Potters in January after number one Asmir Begovic broke a finger but has been back on the sidelines since the Bosnian's return.
Butland spent three months on loan at Leeds' Yorkshire Championship rivals Barnsley earlier this season.
Hughes said: "I think there's been further contact (with Leeds) since we came back. We're hopeful that might be concluded. If he can go there and get games then obviously that will help his development.
"He's had a good year up to this point, he's been out on loan already, was able to get games in the first team here, so he's progressing really well.
"Leeds is a big club with big expectations, a good fan base, and with the pressures that brings - he needs to play under that type of pressure to enable him to continue to progress."
Butland had hoped a run of games for Stoke might help him force his way into Roy Hodgson's England squad for this summer's World Cup finals.
Hughes believes that is now unlikely but does not think it is beyond the realms of possibility.
"It's difficult but if he's playing regularly then he'll have an opportunity," said the Stoke boss.
"Certainly he's well regarded by everybody in the England set-up. If he has a run of games and a run of form, then who knows, because his ability is there for everybody to see.
"He's played at Premier League level, which before could have been levelled against him. He's acquitted himself really well so we'll have to wait and see.
"Our motivation is to keep him progressing, and he's going to be an outstanding keeper for Stoke City."