The 20-year-old has been out of action since February, when he damaged his cruciate ligaments while playing for Wolverhampton Wanderers on loan.
"I will be back in full training with the squad on 17th on this month," Frimpong wrote on his Twitter page.
"Two cruciate knee injuries couldn't end my career. It's been a long 7 months."
Arsenal have picked up five points from three matches in the Premier League so far.