The person was struck as they walked along the road near junction 16 at around 5.10am. The road was shut in both directions between junction 16 for Northampton west and Upper Heyford, and junction 15A for Northampton Services and Northampton south. The northbound carriageway has since been reopened.
Traffic is at a standstill southbound and remains affected northbound, according to Google Traffic.
“Emergency repairs” are taking place, Highways England has said.
Northants Live reports police are investigating the fatal crash, which traffic information service Inrix says involved a lorry.
A spokesman for Northamptonshire Police said: “An investigation into the incident has been launched and, as a matter of urgency, officers would like to hear from anyone who may have seen a pedestrian walking along the carriageway earlier today.
“Officers are also appealing to anyone who was travelling on this stretch of the M1 to check their dash-cam footage to see whether they have unknowingly captured the incident.
“Anyone with information or anyone who witnessed this incident is asked to call the Drivewatch Hotline on 0800 174615 or Northamptonshire Police on 101 quoting reference number 30 of 25/08/21.”
Ambulance crews also attended the collision, it is reported.
At the time of the incident, National Highways posted on Twitter: “The #M1 southbound #J16 (#A4500 #Northampton) to #J15A / Northampton Services (#A43 #Northampton) is in the process of being CLOSED due to a serious collision.
“Traffic Officers @NorthantsPolice @EMASNHSTrust & Maintenance Crews are on their way to the area.”
Southbound drivers are leaving at Junction 16 to join the A45 and then use the A5 southbound through Weedon Bec, but this area is congested.
Local roads in Northampton are also slow as a result of the crash.