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Police were called to the M20 following a hit-and-run.
Officers were called at around 6.40am after a collision between a car and a van on the London-bound carriageway near Wrotham.
Motorists were left waiting as traffic was held between junction 1 and junction 2 for the A20 London Road, near Brands Hatch at around 7.45am as police attended.
Police spokesman Steve Knight said: "The driver of one of the vehicles was reported to have left the scene following the incident.
"Officers attended and stopped the traffic before carrying out a search of the area."
They are still searching for the man.
Highways England confirmed traffic was moving again at 8.20am.
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