Frimpong picked up his injury during a loan spell with Fulham, being forced off during the 3-0 victory over Swansea City on the final day of the season.
The Ghanaian has struggled with a number of injuries in his career and he made only five appearances for Wolves in 2012 before he suffered a previous knee injury which also required surgery.
The 21-year-old was scheduled to represent his country during the summer as they aim to secure qualification for the 2014 World Cup in Brazil.
Frimpong tweeted: “I had surgery yesterday night and am expected to be out for 8 weeks. It saddens me that I couldn’t go play for Ghana in the World Cup qualifiers next month but i wish the coach and the players good luck for the matches.
“I Hope we get maximum points from the games. I wanna thank everyone at Fulham for their support but it is a great feeling to be back at Arsenal.”