Police said the driver's blue Ford Mustang hit a woman and then a building around 1:20pm.
According to investigators, the woman was riding her bicycle on the North Loop at North Main. She was crossing an intersection when the Mustang struck her, officials said.
Rick Halliburton witnessed what happened. He said several people were waiting at the red light. He watched the woman make her way across the intersection and then saw the Mustang weave through traffic and hit her.
"He did not even stop he sped up," Halliburton said. "He tried to pass the truck on the right and then when he tried to pass, he caught the rear end of her bike and flipped her."
Witnesses told police the driver then sped away.
Several people tried to follow the car, but could not keep up.
He eventually lost control and crashed into a metal building in the 8900 block of North Main at Crosstimbers, damaging machinery and equipment inside.
Witnesses told us the driver was speeding, and he came close to hitting several other cars just before he struck the cyclist.
"I saw the Mustang. He came across the tracks, he passed me, he come up here, he was running about 60 or 70 [mph]," Tommy Deveaux said. "I thought he was going to lose it right up here in front of the school, but after that I didnt see him anymore."
The bicyclist was alert when emergency responders took her to Ben Taub General Hospital, officials said. At last check, she was stable.
The driver was also transported to Ben Taub in unknown condition. He now faces charges.
No one else was injured. No names have been released.
The accident remains under investigation. Police said they do not believe alcohol played a role.