Ralph Mothes, 59, and Paloma Werner, 50, were helpless as the beast thrashed around on their 33ft vessel before slipping back into the water.
Miss Werner said: "It really was quite incredible but very scary. The whale was about the same size as the boat.
"We'd spotted it about 100 metres away and thought that was the end of it. Then suddenly it was right up beside us.
"I assumed it would go underneath the boat but instead it sprang out of the sea. There was hardly any wind, so we couldn't get out of the way. We didn't have time to take any evasive action. We were very lucky to get through it, as the sheer weight of the thing was huge.
"There were bits of skin and blubber left behind, and the mast was wrecked. It brought down the rigging too.
Moments before the animal leapt it had pounded its tail on the surface of the water in a 'lob-tailing' ritual to communicate with other whales.
The shaken couple, who are experienced seafarers with the Cape Town Sailing Academy, used their engine to get back to shore in Table Bay.
However, officials are now investigating whether the whale was being provoked before it breached.
The manager of the local Waterfront Boat Company, Richard Smith, said that some of his crew members who had been conducting a whale-watching tour said that they saw a yacht harassing the whale prior to the incident.
'They said the yacht kept coming to the whale. Speeding straight at it and annoying it,' he said.
By law, boats in the area must keep 300m away from whales, and must take evasive action to avoid them.
Whales are a common sight in the Atlantic Ocean off the Western Cape coast at this time of year as they come near the shore to breed.
Thousands of tourists flock to the region's seaside resorts every year to spot the mammals during the South African winter from June to November.
Hermanus, a popular destination around 80 miles east of Cape Town, employs a 'whale crier' to walk through the town announcing where whales have been seen.
Sources: Telegraph, Metro.co.uk
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