A Vauxhall Corsa collided with a BMW and then the garden of a property in Highgate, Upper Gornal, just after 11am on Sunday, said West Midlands Police.
The driver of the Corsa ran off, while the driver of the BMW was not seriously hurt.
Police said the Corsa had been stolen overnight in Dudley between May 30 and 31.
Enquiries led to the arrest of the teenager, from Upper Gornal, on Monday morning.
A spokesman for the force said: "He’s been questioned on suspicion of car theft and released under investigation while enquiries continue."