A fit Forrester would probably have toured South Africa with England this summer and then challenged for a World Cup berth during the pre-tournament Tests in August.
Gloucester head coach Dean Ryan said: "This is obviously devastating news for James and for Gloucester, particularly at this stage of the season when we are chasing play-offs and semi-finals.
"It is also likely he will miss out on a place in the World Cup, and that is exceptionally bad luck for a wonderfully gifted individual who is capable of changing the face of a game.
"Everyone associated with the club wishes James the very best in his recovery, and we are right behind him."
Forrester, whose career has been dealt repeated injury setbacks, was hurt during the first half of Gloucester's 35-13 victory at Ashton Gate.