The Manchester United centre-half, brother of Johnny, sustained the injury in Monday's 1-1 draw at QPR and will miss Saturday's final home game against Cryatal Palace at the KC Stadium.
The 20-year-old, who has made 17 appearances for Nigel Pearson's side since arriving in January, is hoping to return to full fitness for the last game of the season at Bristol City but fellow defender Liam Rosenior will play no further part this season.
The full-back damaged medial knee ligaments in last week's home defeat to Middlesbrough and although he does not require surgery, the 26-year-old will not be available for the last two matches.
Source: PA
Source: PA