Residents say the collision happened near speed calming measures in High Street, Eye, at around 2.30am.
An eye witness said a stationary vehicle was also damaged in the crash and that the occupants of the car were not seriously injured.
The eye witness said the two occupants got out of the vehicle.
The collision happened outside the property of resident Dale McKean.
Mr McKean said: “It was a rude awakening at 2.30am on my birthday!
“There was a loud crash and a bang. The car had bashed into my neighbour’s oak arched entrance, which is part of a grade 2 listed building,
“A neighbour’s car was also struck and the crashed vehicle had gone through the traffic calming chicane.
“It was a right mess, and was very concerning. Leaked fuel looked to have been mopped up and that was very near residential properties.”