The attack occurred around 9 a.m. about 100 yards offshore from the Beach Safety Center at 17th Street, according to the city.
"The victim was transported by ambulance to Scripps Memorial Hospital La Jolla with injuries that are significant but not believed to be life-threatening. The injuries included bites to the torso, left arm and hand," the city reported.
Lifeguards temporarily closed beaches for swimming and surfing one mile in both directions from the incident, roughly from Sixth Street to North Beach. A water closure will remain in effect until at least 9 a.m. Tuesday.
The victim was in a group of about a dozen swimmers who meet regularly to train in Del Mar, city officials said.