The bumper of the blue Vauxhall Corsa was ripped off during the collision.
Crews from Walsall Fire Station were called out to the incident on Friday.
The driver, who was allegedly under the influence, is thought to have abandoned the vehicle.
The tree was left with 'minor damage', firefighters said.
Walsall Fire Station tweeted: "#greenwatch busy evening- we attended this incident , the driver was under the influence and decided not to hang around,the tree suffered minor damage #fatal4."