One of London's most popular sites, the massive vessel was "100 percent" ablaze, according to Britain's Sky News, which quoted fire officials.
Eight fire trucks battled the flames.
Speaking to the British Broadcasting Corporation on his way to Greenwich, where the Cutty Sark is docked, the Chief Executive of the Cutty Sark Trust said, "we're losing history itself."
Richard Doughty expressed the most concern over the quantities of original fabric aboard the ship, which has been closed to the public for months during a $50 million renovation. It was due to be reopened in 2009.
"When you lose original fabric, you lose the touch of the craftsman, you lose history itself," he said.
CBS News correspondent Sheila MacVicar reports that one fact gave the Cutty Sark conservation crew hope Monday morning: about 50 percent of the material from aboard the ship was safely stored off-site during the blaze, due to the renovation work.
Fire officer Ian Allchin told the BBC that the fire had been brought under control, but it was "quite a well-developed fire when we arrived", and there was extensive damage.
Doughty had said the fire was being treated as "suspicious", but Allchin would not confirm that classification, saying only the investigation was ongoing.
MacVicar reports that the main concern of the Cutty Sark's renovation crew is now the original, iron skeleton of the clipper. Some British media have reported already that some of the iron beams were warped by the heat. If that is the case, it could make restoring the ship to its original condition very difficult.
The vessel is sometimes referred to as "the Ferrari" of yesterday's seas. It was designed to be — and was then praised for being — much faster than any of its contemporaries.
The Cutty Sark sailed numerous trips in its heyday to retrieve tea from China and wool from Australia. It's a valuable piece of British history, and one of London's major tourism attractions. The ship was built in 1869.
Doughty said: "In terms of world maritime heritage, she is one of, if not the most important ship."
"She's part of our national identity," he added.