Van Persie suffered extensive ligament damaged whilst playing for Holland against Italy earlier this month.
A club statement said: "Robin Van Persie returned to Arsenal on November 22nd following an ankle injury sustained whilst on international duty with Holland.
"The injury was expected to keep him out of action for between four and six weeks.
"Upon his return, the Arsenal medical team conducted a thorough review of his scans, his early injury management and the treatment he had received.
"Having scrutinised these in detail and assessed the response of his ankle, the Club's medical team concluded that further investigation and opinion was required.
"Advice was sought from the leading ankle specialist Mr Niek van Dijk, who confirmed that more extensive damage had been suffered than was first diagnosed.
"In order to repair his ankle, Robin will undergo surgery next week in Amsterdam to reconstruct the ligaments. The Club's medical team anticipate that a full recovery will take between four and five months."