The 31-year-old, who is on loan from Aston Villa, suffered the problem during Saturday's 2-0 defeat at Fulham.
Bent, who joins John Eustace, Chris Martin, Zak Whitbread, George Thorne and Mason Bennett in the treatment room, is now expected to be out of action until the start of April.
Derby continue their bid for promotion to the Premier League on Tuesday when they travel to Brighton & Hove Albion.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| C | Portsmouth | 46 | 28 | 13 | 5 | 78 | 41 | 37 | 97 |
| P | Derby CountyDerby | 46 | 28 | 8 | 10 | 78 | 37 | 41 | 92 |
| 3 | Bolton WanderersBolton | 46 | 25 | 12 | 9 | 86 | 51 | 35 | 87 |
| 4 | Peterborough UnitedPeterborough | 46 | 25 | 9 | 12 | 89 | 61 | 28 | 84 |
| 5 | Oxford UnitedOxford Utd | 46 | 22 | 11 | 13 | 79 | 56 | 23 | 77 |
| 6 | Barnsley | 46 | 21 | 13 | 12 | 82 | 64 | 18 | 76 |
| 7 | Lincoln CityLincoln | 46 | 20 | 14 | 12 | 65 | 40 | 25 | 74 |
| 8 | Blackpool | 46 | 21 | 10 | 15 | 65 | 48 | 17 | 73 |
| 9 | Stevenage | 46 | 19 | 14 | 13 | 57 | 46 | 11 | 71 |
| 10 | Wycombe WanderersWycombe | 46 | 17 | 14 | 15 | 60 | 55 | 5 | 65 |
| 11 | Leyton Orient | 46 | 18 | 11 | 17 | 53 | 55 | -2 | 65 |
| 12 | Wigan AthleticWigan | 46 | 20 | 10 | 16 | 63 | 56 | 7 | 62 |
| 13 | Exeter CityExeter | 46 | 17 | 10 | 19 | 46 | 61 | -15 | 61 |
| 14 | Northampton TownNorthampton | 46 | 17 | 9 | 20 | 57 | 66 | -9 | 60 |
| 15 | Bristol Rovers | 46 | 16 | 9 | 21 | 52 | 68 | -16 | 57 |
| 16 | Charlton AthleticCharlton | 46 | 11 | 20 | 15 | 64 | 65 | -1 | 53 |
| 17 | Reading | 46 | 16 | 11 | 19 | 68 | 70 | -2 | 53 |
| 18 | Cambridge UnitedCambridge | 46 | 12 | 12 | 22 | 39 | 61 | -22 | 48 |
| 19 | Shrewsbury TownShrewsbury | 46 | 13 | 9 | 24 | 35 | 67 | -32 | 48 |
| 20 | Burton Albion | 46 | 12 | 10 | 24 | 39 | 67 | -28 | 46 |
| R | Cheltenham TownCheltenham | 46 | 12 | 8 | 26 | 41 | 65 | -24 | 44 |
| R | Fleetwood TownFleetwood | 46 | 10 | 13 | 23 | 49 | 72 | -23 | 43 |
| R | Port Vale | 46 | 10 | 11 | 25 | 41 | 74 | -33 | 41 |
| R | Carlisle UnitedCarlisle | 46 | 7 | 9 | 30 | 41 | 81 | -40 | 30 |
| > League One Full Table | |||||||||
