The deadly crash happened just before 11:30 p.m. on the East Freeway. According to police, a family was driving home when a disturbance broke out inside the car.
HPD didn't say how many people were in the car or what the argument was about.
At one point, the driver pulled over to the left shoulder after a woman inside the car asked to get some fresh air, according to authorities.
Police said that is when she stepped out into a moving traffic lane and was struck by a driver, who stopped immediately.
Officials said the driver who hit the woman showed signs of intoxication and was detained for a possible DWI.
The crash remains under investigation, HPD said.