The younger teen is expected to survive, KTRK reported.
The names of the two teens have not been released.
Houston police Sgt. David Rose said he did not believe alcohol was involved and could not say if the driver was speeding, KTRK reported.
Rose said he was “not sure” if the driver was wearing a seat belt.
“I suspect the driver was not,” Rose told the television station. “I believe the passenger was wearing a seat belt."