The shooting was reported at the Jack in the Box at Valley Boulevard and Fremont Avenue.
The deputy was rushed to Los Angeles County + USC Medical Center, where he is in critical condition, according to LASD Sheriff Alex Villanueva. A large contingent of sheriff's deputies converged at the hospital.
The deputy was off-duty at the time of the shooting, sheriff's officials said at a 10 p.m. news conference. The unidentified 13-year veteran deputy was in civilian clothes and ordering food when the suspect went up to him and shot him once in the back of the head, officials said.
The shooting was caught on video, according to sheriff's officials. The suspect was also caught on a surveillance camera from a nearby home. He was seen changing clothes after the shooting and is believed to be in a black T-shirt and black jeans.
The suspect's vehicle is believed to be a white 2006 Kia Sportage with paper plates.