Police say the car chase started as a traffic stop at 5398 Jason Street at about 1:40 p.m.
HPD said the suspect squeezed his vehicle onto a pedestrian bridge along the bayou and hit a man who was part of a landscaping crew.
Officers said the man was alert and talking when he was taken to the hospital but his condition is unknown.
According to police, they found guns, money and drugs in the car.