The 26-year-old will miss the start of the new season after suffering the injury in training recently in what is a setback for both the side and the player.
Parry missed the end of last season due to a chest injury but had hoped to be fully fit and available for the new campaign, which kicks off in September.
Ospreys said in a statement on their website: 'Following this week's surgery he is now looking at a possible four-month lay-off.'
Parry has made 78 appearances for Ospreys since joining from Newport Gwent Dragons in 2014.
Ospreys have also confirmed they will play a pre-season friendly against Northampton Saints on August 11 in Brigend as they continue to prepare for the new season.