The incident happened at about 1.15pm – and the lorry was still alight just before 4pm as firefighters tried to wet down the flames.
Southbound queues stretch back to junction 30, with northbound delays back to junction 26.
Highways England traffic officers have been on scene, and helped to release trapped traffic via the Tibshelf services.
Lanes one and two northbound have been damaged by fire. Highways England will now work to repair the damage – however, this is likely to last overnight. We are expecting delays to continue through past peak times this afternoon, so drivers should use alternative routes wherever possible.
Diversions have been set up: southbound diversion signs are marked with a black square, and the northbound diversion signs are marked with a black triangle.
The southbound diversion takes drivers off at junction 29, onto the A617 towards Mansfield, then onto the A6075 southbound onto the A38 westbound towards Derby, to rejoin at J28.
The northbound diversion takes drivers off the M1 at j28, onto the A38 eastbound towards Mansfield, onto the A6075 northbound towards Mansfield, then onto the A617 westbound to rejoin the M1 at j29.
For the latest updates, follow @HighwaysEMIDS on Twitter, or check the Traffic England website.
Members of the public should contact the Highways England customer contact centre on 0300 123 5000.
Journalists should contact the Highways England press office on 0844 693 1448 and use the menu to speak to the most appropriate press officer.