"We haven't got the scans back yet, but he will probably be out for four to six weeks, it's a sore one" said Blades chief Robson, who replaced Neil Warncok in the summer.
"We could have done without this, at this time of the season you need your best players out on the pitch.
"It's a massive blow because all season James has scored goals, although we have Rob (Hulse) coming back and we also have Jon (Stead) and Billy (Sharp) up there."