The 19-year-old striker saw his previous short-term deal at Bootham Crescent expire on January 4.
Morris, who spent the early part of the campaign on loan at Oxford United, has made four appearances for York so far this season.
The teenager is yet to play a senior game for parent club Norwich.
York are back in League Two action on Saturday when they travel to Wycombe Wanderers.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Ipswich TownIpswich | 43 | 26 | 11 | 6 | 85 | 53 | 32 | 89 |
| 2 | Leicester CityLeicester | 42 | 28 | 4 | 10 | 79 | 38 | 41 | 88 |
| 3 | Leeds UnitedLeeds | 43 | 26 | 9 | 8 | 76 | 34 | 42 | 87 |
| 4 | Southampton | 42 | 25 | 9 | 8 | 84 | 54 | 30 | 84 |
| 5 | West Bromwich AlbionWest Brom | 43 | 20 | 12 | 11 | 66 | 42 | 24 | 72 |
| 6 | Norwich CityNorwich | 43 | 21 | 8 | 14 | 76 | 60 | 16 | 71 |
| 7 | Hull City | 42 | 18 | 11 | 13 | 62 | 54 | 8 | 65 |
| 8 | Coventry CityCoventry | 42 | 17 | 12 | 13 | 66 | 52 | 14 | 63 |
| 9 | Middlesbrough | 43 | 18 | 9 | 16 | 61 | 56 | 5 | 63 |
| 10 | Preston North EndPreston | 43 | 18 | 9 | 16 | 56 | 60 | -4 | 63 |
| 11 | Cardiff CityCardiff | 43 | 18 | 5 | 20 | 48 | 60 | -12 | 59 |
| 12 | Bristol City | 43 | 16 | 10 | 17 | 50 | 46 | 4 | 58 |
| 13 | Sunderland | 43 | 16 | 8 | 19 | 52 | 50 | 2 | 56 |
| 14 | Swansea CitySwansea | 43 | 14 | 11 | 18 | 53 | 62 | -9 | 53 |
| 15 | Watford | 43 | 12 | 16 | 15 | 59 | 58 | 1 | 52 |
| 16 | Millwall | 43 | 13 | 11 | 19 | 42 | 55 | -13 | 50 |
| 17 | Blackburn RoversBlackburn | 43 | 13 | 10 | 20 | 57 | 71 | -14 | 49 |
| 18 | Plymouth ArgylePlymouth | 43 | 12 | 12 | 19 | 58 | 66 | -8 | 48 |
| 19 | Queens Park RangersQPR | 43 | 12 | 11 | 20 | 40 | 57 | -17 | 47 |
| 20 | Stoke CityStoke | 43 | 12 | 11 | 20 | 41 | 60 | -19 | 47 |
| 21 | Birmingham CityBirmingham | 43 | 12 | 9 | 22 | 48 | 64 | -16 | 45 |
| 22 | Huddersfield TownHuddersfield | 43 | 9 | 17 | 17 | 47 | 70 | -23 | 44 |
| 23 | Sheffield WednesdaySheff Weds | 43 | 12 | 8 | 23 | 36 | 67 | -31 | 44 |
| R | Rotherham UnitedRotherham | 43 | 4 | 11 | 28 | 32 | 85 | -53 | 23 |
| > Championship Full Table | |||||||||
