Police said they believe it was launched from the rear of a red Vauxhall Cavalier car that was parked in Queen Street at about 0015 BST.
The device struck a wall but did not explode. Police are investigating a link with dissident republicans.
A Fold for the elderly and a number of other houses were evacuated as a precaution. No-one was injured.
It is understood the device partially exploded inside the car which was found on fire. A bomb disposal team later carried out a controlled explosion.