Nunez allegedly poured a flammable liquid on his girlfriend, 28-year-old Maribel Rebolledo, on Saturday night and setting her on fire. The reason behind the incident was unknown.
Rebolledo has burns over 60 percent of her body.
Anyone with information on Nunez's whereabouts is urged to call L.A. County Sheriff's arson detectives at (323) 881-7500.