Anita was replaced in the 27th minute of this afternoon's game, decided in West Bromwich Albion's favour by a 78th-minute goal from Darren Fletcher.
The midfielder will be assessed tomorrow, but head coach Steve McClaren fears that Anita will miss a number of games.
Asked about the severity of the injury, McClaren said: "I think it's a bad one.
"We'll have to assess him. He's been great for us."
McClaren whose relegation-threatened side take on second-placed Arsenal at the Emirates Stadium on Saturday is already without a number of players because of injury.
However, defender Jamaal Lascelles was back on the bench at The Hawthorns after recovering from a hamstring problem.