Twenty-two fire engines were called at about 03:20 BST to the Regent Superbowl and indoor market in Great Yarmouth.
The fire took almost seven hours to put out and an investigation into the cause is under way.
Town leaders have described the loss of the popular landmark at the height of the summer season as a "tragedy".
A spokesman for Regent Superbowl, which opened 53 years ago, said it was the oldest working bowling alley in the country.
He said: "A significant part of tenpin bowling history has been lost. This is a very sad time for our business, as well as the Great Yarmouth community."
Great Yarmouth Borough Council leader Graham Plant said it was a "real blow" to the town.
He said: "The Regent 'Bowl has been there for so many years now and it's so popular. A lot of people will miss it and it's a real tragedy for the town, it really is, I'm absolutely devastated."
The blaze engulfed the Regent Road building, causing it to partially collapse.
At its height, 88 firefighters tackled it and the plume of smoke could be seen up to 11 miles away in Acle and Lowestoft.
David Ashworth, assistant chief fire officer for Norfolk, said: "The fire developed quite rapidly where there was a sudden in-rush of air. That would have been a consequence of one of the roller shutters becoming displaced or falling or as a consequence of the roof structure giving way.
"That would have allowed a sudden in-rush of air, particularly oxygen, which enhances the intensity of the fire considerably."
More than 100 homes were left without power while UK Power Networks made the area safe.
Meanwhile, traders who operate from the building said they were "devastated".
Stephen Cook, who runs a memorabilia stall, said he had up to Â£150,000 worth of uninsured stock there.
"Everything which has taken me the last three years to build from scratch has gone overnight," he said.
Town leaders have described a fire that destroyed a popular landmark at the height of the summer season as a "tragedy".