Hills, who impressed at left-back this season before moving to a more advanced midfield role, pulled up midway through the first half against Luton.
The former Gillingham player has been one of the most consistent members of the squad this season and his loss for the big games against Millwall, Coventry and Crystal Palace will be a major one.
It looks very doubtful if he will be back for the Blades' clash on February 18 but a more realistic target is Southampton away on the following Saturday.