The 24-year old Brazilian sustained the injury in the first half of Saturday night's 2-0 loss to Sydney FC and had to be replaced immediately.
It looks as though Robson may miss the remainder of the 2010/11 campaign, prompting United coach Miron Bleiberg to look for a replacement leading into the finals.
"It's not a lucky period for us. Robson has had his injury problems in the past but we nursed him through and used him sparingly knowing we would need him while Jason (Culina) was away," said Bleiberg.
"He injured his hamstring against Sydney and the likelihood is that it will sideline him for the majority of the season. We are hopeful of signing (Nuremberg midfielder) Peter Perchtold but Peter is more a central midfielder than a playmaker.
"Time is against us a little at the moment but we will certainly be looking at some options. If we can find a replacement for Robson, someone who can perform in that playmaker role, then that's the course of action we will take.
"If the right player comes along then the door is open, not just for the rest of this season, but possibly next season as well."