The centre-back, 32, suffered the problem on Saturday as the Blades were beaten 1-0 by Coventry City.
"It's a massive blow for both Chris and the club and realistically we won't see him in action again until pre-season training next July," said the United manager Gary Speed.
"The lads we have that can play in the central defender's role will miss his experience and spirit, but I'm sure they will do all in their power to make up for his absence."
Queens Park Rangers have signed midfielder Georgios Tofas until the end of the season.
The Cypriot, 21, is a free agent after being released be Anathorsis Famagusta.
"He looks like our type of player - he can take men on, yet he knows he has to work hard for the rest of the team. He has got the right work ethic," said Neil Warnock, the R's manager.
"The chance to bring him in until the end of the season was too good an opportunity for me to turn down."
Watford have said they expect the rugby union side Saracens to end their groundshare with them at the end of the season.
Sarries, who play in the Premiership, have played their home games at Watford's Vicarage Road ground since 1997.
Nottingham Forest have opened talks with forward Robert Earnshaw over a contract extension.