The crash happened at about 03:25 GMT near junction 16 northbound.
Northamptonshire Police, who had been investigating the theft of a vehicle, said the man stopped in the road and ran across the southbound carriageway when he was hit.
The Independent Police Complaints Commission has been notified.
Live updates on the crash and other Northamptonshire stories at BBC Local Live.
The southbound carriageway remains shut between junctions 18 and 16, but two lanes have reopened northbound.
Queues southbound have been backed up to Lutterworth in Leicestershire, with knock-on effects also spreading to the nearby M6, A14, A5 and the M45.
One driver told the BBC he had been stuck in M1 queues for four hours.
Accident investigators were examining the closed section and oil was being cleared from a carriageway.
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Northamptonshire Police and Crime Commissioner, Adam Simmonds, said: "I am aware of the tragic incident on the M1 this morning and await the results of the police investigation and the view of the IPCC."
BBC reporter Martin Heath, who was close to junction 16, said the motorway was completely empty and there was stationary traffic on local roads "as far as the eye can see".
He added there was no immediate sign of the situation changing, adding "everyone is being affected by this".
A driver who police were chasing on the M1 near Northampton has died after he got out of the car and was hit by another vehicle.