The Dutchman, who is Arsenal’s leading scorer this season, sustained the injury, when celebrating his goal in the 2-1 win over Manchester United yesterday.
Gunners boss Arsene Wenger said: “There is a big worry on Robin van Persie.
“He had scored a great goal because first of all Rosicky and (Cesc) Fabregas fought like mad for the ball, then they get it in and Robin comes from a very deep position and scores an unbelievable goal, but he can deliver that.”