The shooting occurred shortly after 1:45 p.m. in the 3400 block of Gregory Drive in the unincorporated community of Bay Point, Contra Costa County Sheriff's spokesman Jimmy Lee said.
Javier-Francisco Valladolid, a 38-year-old Pittsburg resident, reportedly shot his sister-in-law Graciela Gonzalez Gutierrez, 34, and his son Christian Valladolid before shooting himself in the head, Lee said.
Sheriff's deputies found Gutierrez, a Bay Point resident, and Valladolid dead inside the home.
Christian was airlifted to Children's Hospital in Oakland, where he remained in critical condition until Friday when he succumbed to his injuries.
An autopsy is scheduled for Monday.
Investigators believe the shooting stemmed from an ongoing domestic dispute between Valladolid and his wife, who had a temporary restraining order against him. Lee said it remains unclear why he shot his sister-in-law.
"Unfortunately it's one of those cases where we may never know," Lee said last week.