The Blades' top scorer sustained the injury during his side's 1-1 draw with Ipswich last week and was forced off at half time.
Lester will now miss the last league game of the season at Preston this weekend and has also been ruled out of the play-offs should United reach them.
Blades boss Neil Warnock hopes the former Nottingham Forest star will be fit in time for pre-season training.
"He's got to be in a plaster cast for four weeks but we are hopeful he will have recovered in time for pre-season," Warnock told the club's official website.
