The statement reads: "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."
The centre-back was withdrawn during the first half of France's game with Spain, which Les Bleus won 2-1 at the San Siro.
It marked the latest trophy in his glittering career, with Reds team-mates Paul Pogba and Anthony Martial also part of the successful side.
The Reds begin a busy period with an away game at Leicester City on Saturday, kicking off at 15:00 BST.