The 21-year-old Dane picked up the knock in last month's 3-0 derby win over Tottenham and had been expected to miss around a month.
He was quoted in the Daily Mirror as saying: "I will have an operation. I don't know how long I will be out."
Arsenal confirmed the striker was set for a minor operation.
While no specific timeframe has been placed on his rehabilitation, it is hoped Bendtner should have recovered by early December.
Bendtner had just come back from a similar problem when he played against Spurs
Speaking at the time the injury was sustained, Arsenal manager Arsene Wenger said: "We suspect [he will be out for] four weeks.
"Bendtner is a big blow. I played him against Tottenham because he is strong in the air.
"It gives us more variety in our games because we can lose possession, yet still win the next header with Bendtner.
"He makes us dangerous at set pieces and so we can change our game a little bit."