Drivers in the area have been told to expect delays of more than an hour following the incident.
Kent Police say they were called at 2.34am, near the exit for Tonbridge, where a woman with serious injuries was pronounced dead by South East Coast Ambulance Service.
Kent Fire and Rescue Service also attended to extinguish a car fire at the same location.
Police officers are working to establish the full circumstances of the incident, including any possible connection between the vehicle fire and the woman’s death, and have arrested a 31-year-old man from London in connection with her death. He remains in custody.
The A21 is closed to all traffic between the Morley’s roundabout and the Tonbridge bypass while enquiries at the scene continue.
Detectives would like to hear from anyone with information that can assist with their enquiries, particularly motorists who were travelling in the area at the same and may have captured footage on their dash cameras.
Anyone who believes they have information is asked to call Kent Police on 01622 604100 quoting 16-0120.
You can also contact the independent charity Crimestoppers anonymously by calling 0800 555 111 or using the anonymous online form at www.Crimestoppers-uk.org
