Critics of the bill called it discriminatory, because it only bans a part of the shark that's used in Asian cultures.
Shark fins and shark-fin soup are a delicacy in the Chinese community. The fins can sell for $600 a pound, and the soup can cost $80 a bowl.
Conservationists say that 73 million sharks are killed for their fins each year. They said it is particularly cruel because the wounded sharks often are returned to the ocean to die after their fins are removed.
The bill has split the Asian delegation in the Legislature. It was introduced by Assemblyman Paul Fong, D-Cupertino, and was supported by Sen. Carol Liu, D-Pasadena, who said it is needed to protect endangered shark species.
Others disagreed. Sen. Ted Lieu, D-Torrance, noted that the bill would ban only part of the shark while permitting the continued consumption of shark skin or steaks.
Gov. Jerry Brown has not said whether he'll sign the bill.
The Associated Press contributed to this report.