Andrej Kultan and Steve Hopkins were kayaking off the southwest coast of Australia on Saturday when the shark struck.
According to Kultan and Hopkins, the animal's teeth punctured two of the three air chambers keeping the kayak afloat, the ABC reported.
Hopkins said he was holding a paddle at the time of the attack, during which he said the pair were knocked into the water.
"It was pretty close, it was right next to me. I had a paddle in my hand, luckily," he said.
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"It had a swim around, bashed my shoulder, then it went off," he said.
Kultan said the pair plunged into the water after the animal, which he estimated to be about three metres long, went for their boat, the report said.
He said the pair clambered back aboard the sinking kayak and managed to paddle 200 metres back to shore.