According to HCSO, detectives arrested 24-year-old Jorge Luis Perez, who is charged with aggravated assault. Perez was booked into the Harris County Jail, authorities said.
Deputies said they responded to the incident in the 400 block of FM 1960.
According to investigators, Perez and the woman are believed to be in a dating relationship and are both from Arkansas. Deputies say that both were involved in an argument while traveling in a pickup truck.
At some point, authorities say that the woman exited the vehicle while Perez allegedly drove away, then turned around and intentionally hit the woman with the truck before fleeing the scene. She was taken to a hospital, where she was listed in critical condition.
An investigation is ongoing.