She was found outside Bellevue Riviera Apartments on Normandy Street near Woodforest, around 1:15 a.m.
The victim was transported to a nearby hospital where she was pronounced dead.
Harris County Sheriff Ed Gonzalez says in a tweet the motive may have been a robbery.
No information about the shooter has been released. Authorities ask if you have any information, to call Crime Stoppers at 713-222-TIPS (8477).