The incident happened at about 12:30 a.m. Thursday when the car drove past a barricade, its driver fleeing from police.
Austin police reported, in its Twitter feed, that of the 23 reported injured, at least five were injured critically.
KXAN reported that a man and a woman riding on a moped were killed. The injured pedestrians were leaving The Mohawk, a bar, when the vehicle struck them.
Police say the driver fled a police stop, almost striking an officer, before driving down the wrong way of a one-way street, CNN reported.
KXAN reported the driver attempted to flee on foot and was subdued with a stun gun.
The driver was placed in custody shortly after the incident, Austin police stated.