The Tulare County Sheriff's Department said Celaya, 31, was shot by deputies early in the day after a slow-speed chase, the Los Angeles Times reported.
Celaya allegedly killed two men and a woman and injured a boy, who authorities said was about 7, Saturday evening on the Tule River Indian Reservation. Celaya then allegedly fled with his 8-year-old and 5-year-old daughters in a Jeep.
When deputies caught up with him about 20 miles away, near Lindsay, about 2 a.m. Sunday, they tried to get him to pull over over. Deputies said he eventually stopped but fired a gun and officers returned fire.
Sheriff's Sgt. Chris Douglass said Celaya also shot his daughters at some point, though it wasn't clear when. One was being treated for life-threatening wounds, the Times said.
Authorities had not provided a motive for the shootings nor had they identified the victims.
Celaya lived on the reservation and was known to use drugs, authorities said.