Video of after the crash shows flames shooting from two of the vehicles.
Police said the driver of the first car lost control and hit the wall barrier. Then a second car slammed into the first car and took off.
The fire started after a third car hit the first car.
One person was killed, but investigators are trying to find out which car he or she was driving.
"Due to the nature of the injuries, we can't determine the sex or race of the victim," Houston police Lt. Larry Crowson said.