After returning to Manchester on Monday, the 28-year-old was assessed by United's medical staff on Tuesday with tests revealing he is set for a spell on the sidelines.
"Raphael Varane sustained a groin muscle injury in the UEFA Nations League final and has commenced rehabilitation at the club. He will be out for a few weeks," a United statement said.
The news will come as a further blow to manager Ole Gunnar Solskjaer, who is already without captain Harry Maguire.
Maguire has missed the last two games with a calf problem and is unlikely to be fit to face former club Leicester on Saturday despite returning to light training during the international break.
Solskjaer is hopeful that Marcus Rashford will be able to feature against Leicester after coming through a behind-closed-doors game with Blackburn last week.
The 23-year-old played for 60 minutes and has shown no ill-effects after his first match action since the European Championship.
He is yet to play for United so far this season but could be set for a place on the bench on Saturday.