Police Capt. Steve Gallagher says Cort Holbrook was arrested after the confrontation Wednesday afternoon in a Livermore parking lot.
Authorities say two men got out of their cars and appeared to argue before one was stabbed in the midsection.
Gallagher says the victim drove himself to the hospital and later died from his injuries.
The victim, whose name was not released, was in his late 40s.
Gallagher says Holbrook appeared to have an abrasion on his face but refused medical treatment. At the scene, investigators found a knife they believe was used in the stabbing.