The police watchdog has begun an investigation after the BMW hit a bus stop at the junction of Prescot Road and Bell Street in Old Swan, Liverpool at about 4.35am.
Images of the scene show a vehicle with its top cut off and its front end smashed in.
The victim, in his 30s, died in hospital.
Merseyside Police said the male driver of the BMW was arrested at the scene.
A spokeswoman said: “Work is ongoing to confirm the identity of the male and inform his next of kin.
“The incident has been referred to the IPCC.”
Police are required to refer cases that involve a death after they have been in contact with someone to the Independent Police Complaints Commission (IPCC).
An IPCC spokeswoman said: “We were notified of a fatal road traffic incident in Liverpool this morning by Merseyside Police.
“We have begun an independent investigation as initial information suggests the collision was preceded by a short police pursuit.
“We have deployed an investigator to the scene and police post incident procedures.”
A number of roads were closed and motorists were asked to avoid the area while forensic investigators examined the wreckage.
An appeal for witnesses has been issued.