Electric wires from the light were left covering the road after the crash at the junction of Old Walsall Road and the A34 Walsall Road in Great Barr.
Police were called to the scene at around 1.40am on Sunday morning, where nobody had been injured.
A 24-year-old man was arrested at the scene and remained in police custody on Sunday afternoon.
A spokesman for West Midlands Police said: "Officers attended Walsall Road at around 1.40am on December 27 to reports of a collision.
"A car had collided with street furniture. Fortunately nobody was injured.
"A 24-year-old man was arrested on suspicion of drink driving and remains in police custody."
Highways workers were called to make the damaged traffic light safe.