Officers responded to report of a confrontation at a home in the 2200 block of Peppertree Way at about 2:40 p.m., according to Antioch police.
Arriving officers found a 49-year-old Pittsburg man who said he had been in a fight with his son-in-law, Anthony Weaver, 24, of Antioch, police said.
The victim suffered a puncture wound to the chest and was taken to a hospital in critical condition, police said.
Weaver fled the scene before police arrived and had not been located as of Monday afternoon.
He is described as being around 5 feet 11 inches tall and weighing around 280 pounds. He has black hair and brown eyes.
Anyone with information about the case is asked to contact Antioch police at (925) 778-2441.