The 26-year-old man was identified as Ben Kelly, a resident of Santa Cruz County, the county coroner's office said.
Kelly was surfing at Manresa State Beach on the northern end of Monterey Bay around 1:30 p.m. when he was attacked by an unknown shark species, the California State Parks said in a statement.
The water one mile north and south of the attack will be closed for five days. Signs were posted warning beachgoers about the attack. The sign said the attack happened within 100 yards offshore.
"State Parks expresses its deepest sympathy to the family of the victim,'' the statement said.
The amount of surfing and swimming has been steady while local officials close the beach every day between 11 a.m. to 5 p.m. to deter a surge of visitors to the coastline during the coronavirus crisis.
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Bay City News contributed to this report.