The midfielder has been on loan with Premier League peers Wigan this season, and he sustained the injury during Saturday's FA Cup quarter-final victory over Everton.
Wigan boss Roberto Martinez hinted on Wednesday that the 20-year-old would be out for the remainder of the campaign.
And Miyaichi's parent club has substantiated those fears.
"Arsenal Football Club can confirm that Japanese midfielder Ryo Miyaichi will undergo surgery in London on Thursday, March 14," a statement from the Gunners read.
"On loan with Wigan Athletic for the 2012/13 season, Ryo injured his right ankle in the club's FA Cup quarter-final victory against Everton last Saturday.
"Having been assessed by specialists, Ryo will have an operation to repair the damaged ligaments sustained.
"Everyone at Arsenal and Wigan Athletic wishes Ryo a swift return."