Josue Jimenez, 33, allegedly had two handguns and fired one when deputies arrived at the scene in Fillmore, the Los Angeles Times reported.
The Ventura County Sheriff's Department said a deputy fired back at Ramirez, striking him with multiple rounds.
"Deputies quickly realized the shot Jimenez fired was directed at a dog," the agency said in a statement.
The Times said deputies performed first aid on the dog and Jimenez.
Jimenez was pronounced dead at a hospital. The dog died at a veterinary clinic.