Varane, who completed a reported 34 million pounds ($45.76 million) move to United from Real Madrid in the close season, returned to the side following a groin injury in their 3-0 league win at Tottenham Hotspur last Saturday.
However, he sustained another problem in the first half of United’s 2-2 Champions League draw at Atalanta on Tuesday.
“With all the technology now you expect him to be out for four or five weeks with the scans. It’s a blow. Raphael has come in and been really influential,” Solskjaer told reporters ahead of Saturday’s derby clash at home to Manchester City.
“Eric Bailly came in last time and was excellent. That’s why we have a big squad and cope with absentees.”
Solskjaer could also be without central defender Victor Lindelof who is also nursing a training ground injury.
“He’s still a doubt but, hopefully, he can come back in tomorrow and say he’s ready … I would expect him to be ready, put it that way but I can’t promise you,” he said.
Solskjaer added that he was relishing facing City at Old Trafford in front of the home supporters after playing in empty stadiums amid the COVID-19 pandemic.
“It’s a special one. The last time we had a Manchester derby with fans in the stadium the atmosphere was electric, everyone will still remember that one more than dark moments we had,” Solskjaer said of their 2-0 win in March 2020.
“When Scott McTominay scored that goal in extra time it was a special moment. It’s a one-off game, we have to start on the front foot, (be) ready because a lot depends on who gets on the front foot.”