The Houston Police Department said it happened along West Fuqua near Buffalo Speedway at about 10:45 p.m. on Saturday.
According to police, an SUV left the roadway for unknown reasons and hit a tree in the median.
HPD said the driver, 16, and front-seat passenger, 14, ran away but later returned to the scene.
A 14-year-old who was in the back seat remained trapped in the vehicle and died, police said.
The driver was taken to the hospital with non-life-threatening injuries before he was taken into custody on a charge of failure to stop and render aid.