The suspected gunman, whose name hasn't been reported, was cornered in a cul de sac in Spring, Texas, a few miles from where police said three children and two adults were found dead in a home.
A fourth child died after being transported to Memorial Hermann Hospital, Harris County Precinct 4 Assistant Chief Deputy Mark Herman said.
An adult was also injured in the incident, though that person's condition wasn't reported.
Herman said when police arrived at the home on Leaflet Lane, they found a woman and a child shot in the head. It wasn't clear if all victims in the incident had been shot.
Police pursued the suspected gunman for 25 minutes before cornering him in a nearby housing subdivision.
Deputies said the alleged gunman is a relative of the victims.