The England international was forced off after 67 minutes of Saturday's 1-0 defeat to Aston Villa at Old Trafford and will play no part against Villarreal in the Champions League on Wednesday.
Maguire's injury is also set to rule him out of the upcoming international break, and Ole Gunnar Solskjaer fears that the centre-back could be sidelined for a little while longer.
Giving a team news update to the media, Solskjaer said: "Luke [Shaw] has been in today so I'll give him a chance to be involved [against Villarreal], he didn't train with the team.
"Harry [Maguire] is more or less definitely out, it doesn't look good. It's his calf, that might take a few weeks."
Maguire was previously an ever-present in the United defence alongside Raphael Varane, but Solskjaer may now elect to call upon Victor Lindelof for the visit of the Yellow Submarine and subsequent clash with Liverpool.