France s defender Raphael Varane (C) speaks with France s coach Didier Deschamps as he leaves the pitch after getting injured during the Nations League final football match between Spain and France at San Siro stadium in Milan, on October 10, 2021. AFP
The French defender suffered the injury during his country's 2-1 win over Spain on Sunday in the Nations League final.
"Raphael Varane sustained a groin muscle injury in the UEFA Nations League final and has commenced rehabilitation at the club," United said in a statement.
"He will be out for a few weeks."
United captain Harry Maguire is also sidelined by a calf problem leaving Solskjaer without his strongest centre-back pairing.
Eric Bailly, whose one appearance this season came in a League Cup loss to West Ham, or Phil Jones, who has not played since January 2020, could now start Saturday's trip to Leicester in the Premier League.
After a visit to the Foxes, the Red Devils face Atalanta at home in the Champions League before fixtures against rivals Liverpool and Tottenham later this month.
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