The suspect was transported to Scripps Memorial Hospital La Jolla and his condition is unknown at this time. No one else is believed to have been injured in the incident.
Del Mar had invited fans who couldn't get in to the sold-out show to watch the concert on TVs throughout the track, including in the paddock area.
The sheriff's office said the suspect was "down" and had been taken to hospital.
San Diego's FOX 5 reported that a San Diego Sheriff's Department deputy had shot a suspect near the racetrack entrance.
Following the shooting, the concert moved "forward as planned", the racetrack said. "The involved deputies were not injured".