Varane, who joined the Red Devils from Real Madrid for £34million, was substituted shortly before half-time after picking up an injury with no-one near him.
United resume their Premier League campaign with a trip to Leicester next Saturday.
The severity of Varane’s injury is not yet known but Victor Lindelof is likely to slot in with Harry Maguire if it’s worst than expected.
Nevertheless, Ole Gunnar Solskjaer was handed a boost earlier this week.
As Marcus Rashford scored twice in a behind-closed-doors friendly between United and Blackburn Rovers.
The England international has not played competitively since missing his penalty for Three Lions in the final of the European Championship against Italy in July because of a shoulder problem.
He hinted could return for the clash against Leicester at the King Power after the international break.
Rashford told United’s official website:
“It’s good now, I’m pretty much at the end now,”
I feel ready to be back on the pitch. So yes, I‘m just looking forward to the next slot of games – it’s a busy schedule.”