The Uruguay international appeared to injure himself scoring a penalty in PSG's 1-0 Ligue 1 win and was substituted straight afterwards.
The club, who are already without Neymar for the Old Trafford clash due to a metatarsal injury, confirmed the news on Sunday afternoon. Right-back Thomas Meunier will also miss the game.
Earlier boss Thomas Tuchel said: "The club will issue a statement later during the day. In my opinion, the news will not be good
"There is a glimmer of hope. We always hope, but the first exam was not good."
Victory over Bordeaux returned the runaway league leaders to winning ways after their defeat at Lyon, but they struggled in front of goal.
Tuchel said: "We really struggled to score, despite playing an excellent first half.
"We dominated, won back possession well and created a lot of chances.
Midfielder Marco Verratti, who made his return from an ankle injury, said: "We still need to improve. We didn't manage to kill the game off.
"Everyone is impatient for Tuesday's game. It will be magnificent match to be a part of and we have confidence in our own ability.
"We all know that this is a very important match for us and the club. We need everyone to win."