Leon County sheriff's detectives say the male passenger jumped out of the car when they tried to pull the vehicle over, with the driver hitting him as she sped off.
Her getaway ended on Barineau Road in western Leon County, crashing her car into a tree.
Deputies arrested 20-year-old Tereka Evans after a short foot chase.
SGT Chris Chase of the Leon County Sheriff's Office says, "The whole root of this from what we're finding out initially on scene is that both the driver and the passenger suspected they had a warrant for their arrest."
A small amount of weed was found in the car. The passenger suffered a broken arm and head injuries. He was taken to the hospital and not arrested.