The 21-year-old's career has already been characterised by a number of injuries and he has suffered another setback after having to undergo an operation on Wednesday
The Ghana international picked up an injury on the last day of the season against Swansea City, in his final match of a six-month loan spell at Fulham.
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However, the Gunners hope to have Frimpong back in time for the new season, with his rehabilitation now underway.
The Arsenal man made two appearances for Arsene Wenger's first team last term - both in the Capital One Cup - and also spent six weeks on loan at Charlton before moving to Craven Cottage.