Officers were alerted to the discovery between junctions 10 and 9 on the London-bound carriageway of the motorway, near Ashford in Kent, on Tuesday.
Paramedics were also called, but the 32-year-old victim – who has not been identified – was pronounced dead at the scene.
Motorists were redirected and the road was immediately closed while emergency services remained at the scene. It reopened on Wednesday afternoon.
Detectives said they are no longer looking for a silver Nissan Qashqai after a man attended a police station on Wednesday night.
He was detained on suspicion of murder and remains in custody while officers investigate the circumstances surrounding the death.
Detective Chief Inspector Richard Vickery said: “I would still like to hear from anyone who may have seen the silver Nissan Qashqai with registration number KY15 WWX on the M20 between 5.30pm and 6.30pm on Tuesday 20 February 2018.
“In addition, I would like to hear from motorists who have dashcam footage taken between 5.30pm and 6.30pm on Tuesday 20 February of the M20 London-bound carriageway between junctions 10 and 9.
“I would also ask motorists who used the M20 after 6pm on Tuesday to contact us if they believe they experienced anything unusual whilst driving and check their cars for signs of involvement in this incident.”
He added: “We do not underestimate the impact that closing this stretch of the motorway had on people and I would like to thank drivers who were delayed for their patience while we ensured that all evidence was collected before the motorway was reopened.”
:: Anyone who witnessed anything unusual in that area of the carriageway or who has information that could assist the investigation should call the Serious Collision Investigation Unit on 01622 798538, quoting reference 20-0913, or email email@example.com