"City of Cape Town shark spotters had closed the beach a few times during the morning after spotting a shark, and it was closed at the time of the attack," said National Sea Rescue Institute spokesperson Craig Lambinon.
The man, 44, was swimming approximately 50 metres offshore at Clovelly corner at the far end of Fish Hoek beach when he was bitten "numerous times".
Although the species of shark has not yet been identified, Lambinon said witnesses indicated it was a white shark.
His right leg was amputated above the knee, and he had a partial amputation of the left foot.
He was stabilised on the beach before being airlifted to hospital.
Lambinon denied rumours that shark sirens could not be sounded due to the widespread power outage experienced in Cape Town on Wednesday morning, saying that the sirens are battery operated.
People have been urged to exercise caution and not go into the water.
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