The 22-year-old, who is yet to make a league appearance for the Welsh outfit, injured ligaments in his ankle during Swansea's 4-0 friendly win over Plymouth Argyle on Sunday.
Donnelly joined Swansea in 2011 after scoring 20 goals in 50 league outings for Northern Irish outfit Cliftonville and was loaned to Coventry City last season, although he returned almost immediately citing "personal reasons".
The news was confirmed on Swansea's official website on Wednesday, with Donnelly requiring an operation that will likely see him out of action until October.
However, there was better news for the Spanish trio of Angel Rangel, Jordi Amat and Chico Flores.
The club reported that Rangel looked to have recovered from a dead leg and could be in line to feature in Saturday's friendly against Reading.
Amat and Flores, meanwhile, are hopeful of returning to training next week as Garry Monk prepares for his first full season at the helm in the Premier League, starting at Manchester United on August 16.
