The driver of a Nissan Micra failed to stop when seen "driving suspiciously" on the northbound carriageway near junction 10 at about 11:55 BST on Saturday, Gloucestershire Police said.
He crashed into a ditch when leaving the motorway near Strensham services, whilst still under pursuit.
The crash has been referred to the Independent Police Complaints Commission.
A motorist died following a police pursuit on the M5 in Worcestershire.