At least two bull sharks were spotted in the Shelly Beach area, in northern Sydney, after the attack and authorities closed all nearby beaches as a precaution.
BBC reports the injured dolphin circled the shallow waters but eventually beached and died.
Manly Open Surf, a carnival taking place at the beach over the weekend, has been suspended.
Lifeguards cleared people from the water after the attack, which happened at around 07:00 local time on Saturday (20:00 GMT on Friday).
Hundreds of people had been about to compete in the festival.