Raphaël Varane, 28, was brought to Manchester United as a heavy defensive reinforcement.
The recruitment has meant that Swedish Victor Nilsson Lindelöf has sometimes been sent to the bench.
The Frenchman is now injured and is expected to miss about a month of play, Manchester United announces.
It was in yesterday's match against Atalanta that the accident occurred.
The midfielder was replaced in the 36th minute.
"We want to wish Raphaël all the best when he works to get back", the club writes.
The injury also means that Varane will miss France's World Cup qualifiers against Kazakhstan and Finland later in November.
For United, a derby against Manchester City awaits on Saturday.
Then Nilsson Lindelöf can get the chance.