Pablo Ramirez, 37, was hospitalized with a gunshot wound to the chest. He was severely wounded, but is expected to survive.
The sheriff's department says a Napa police officer fired at the suspect when he tried to arrest him.
"I was in the restaurant eating I heard the ambulance come," witness Frank Lancendoeffer said.
Lancendoeffer was having dinner at the Black Bear Diner on Gasser Drive when a gunshot was heard and suddenly, police converged on the parking lot across from a Home Depot.
A Napa County undercover narcotics team was watching a car with three men inside, including one of the suspects, Ramirez.
"They approached the vehicle to go ahead and arrest the suspect with the warrant for violation of probation on an assault with a deadly weapon case, and a struggle ensued between one of the officers and that suspect and a shot was fired," said Napa County Sheriff's Department spokeswoman Capt. Tracey Stuart.
The sheriff's department says Ramirez was wanted on a probation violation after trying to kill his wife with a 7-inch knife.
The shooting has left Lancendoeffer rattled. He says Napa has changed. "When I was a kid growing up here, you used to be able to go to bed at night with your front doors open and unlocked, you know, screens unlocked. People didn't care. You could sit out on your porch at night and now, it's not safe for people to walk around the streets anymore for fear that somebody is going to get mugged or robbed, or shot," he said.
The Napa County Sheriff's Office is investigating the incident. Police say the officer involved was not hurt, but has been placed on administrative leave following standard procedure in the event of an officer-involved shooting.
Ramirez remains hospitalized and may face new charges of assault on a police officer.