Police say the attempted robbery happened in the early morning of March 18 in the 8400 block of the Gulf Freeway service road.
The woman told police a man in an older model white sedan with black headlights pulled up next to her and offered her a ride.
After getting into the front passenger seat, that's when the suspect allegedly pulled out a handgun and demanded all her belongings. As the suspect continued down the road, the woman was shot as she opened the door to jump out, police said.
Surveillance video shared by the Houston Police Department shows the suspect's vehicle and a sketch of the man.
The suspect is described as a Black man with tattoos on his neck, last seen wearing an earring on his right ear.
If you know any information regarding the suspect's whereabouts, you are urged to contact Crime Stoppers at 713-222-8477.