The “incredibly unpleasant” discovery was made between junctions 16 and 17 near Rugby.
Serveral vehicles ran over the body before traffic was brought to a halt, cops say.
Police have closed the northbound carriageway and say it will be closed most of today.
Highways England said this was a “serious incident”.
Sgt Tony Hopkins said: “We need to find out where the person came from and why they were on the M1. We are trying to work out what happened.”
Northamptonshire Police added: “Motorists are advised to seek alternative routes and diversions will be in place.”
Frustrated drivers snapped photos of the deadful traffic as it increased throughout the morning.
Traffic was so bad that some motorists were forced to relieve themselves in public on the side of the road.
But Highways England also tweeted that they were dealing with a spillage which was causing traffic for southbound travellers on the M1.
“S/B btwn J13 + J12 we’re clearing spillage from 4 lorry collision. Pls allow extra travel time will affect traffic for,” they tweeted.
They have advised drivers heading northbound to exit at junction 16 and follow the hollow triangle symbol via the A45 westbound and A5 northbound and then the A428 eastbound and A5 eastbound to rejoin the M1 at junction 18.