Robinson dislocated his shoulder twice in the match, with surgery recommended as the best option to ensure a full recovery in the long term.
The 21-year-old should return via the NEAFL by Round 19-20, meaning a return to the senior side this year appears unlikely.
The young midfielder played four matches last season, before playing every game this season prior to his injury.
“It was a tough break,” Sydney general manager of football Tom Harley said.
“He’s a young player who was really starting to make inroads in his career, so there’s certainly no rush to do anything drastic.
“We’ll be conservative, he’s got a lot of footy to go (in his career).
“It’s unfortunate for him given he’s played a lot of senior footy this year, but I’m sure he’ll recover well.”