Police said that two woman and a man were taken to trauma centers with significant injuries, but none are life threatening and are expected to survive.
One of the women was the operator of the bicycle taxi and the two other victims were her fare.
The accident happened around 9:40 p.m. at the intersection of Austin and Capitol Streets.
The taxi was going westbound on Capitol when an unknown car hit the bicycle, police said. Witnesses saw the vehicle but were unable to identify it.
Anyone with information on the incident is urged to contact the HPD Hit and Run Unit at 713-247-4072 or speak anonymously to Crime Stoppers at 713-222-TIPS.