The collision took place at about 7.35pm yesterday evening (Monday October 21) at junction 21a of the northbound carriageway near to the junction with the A46 and involved a pedestrian and a HGV.
The pedestrian, a man, received serious injuries and subsequently died.
The M1 motorway which was closed at junction 21 northbound up to junction 22 has now been re-opened.
Leicestershire Police have thanked those motorists who were unfortunately caught up in the tailbacks for their patience whilst the emergency services dealt with the incident.
Anyone who witnessed the collision is asked to contact Leicestershire Police on 101 or Crimestoppers, on 0800 555 111.