There are claims police are threatening people who are spreading pictures and news about the blaze.
The fire erupted at the Jokhang Temple in the Tibetan capital of Lhasa at about 6pm, state broadcaster CCTV reported. "The fire was quickly extinguished, there are no casualties and order is normal in its environs", the newspaper said on its WeChat account.
But on Twitter, which is blocked in China, Tibetans overseas noted that photos and posts about the fire were quickly being censored.
Footage believed to have been posted on Twitter by United States government-backed Radio Free Asia shows the upper part of the temple engulfed in red flames, and water being sprayed from a distance. The incident occurred during the Losar festival, which celebrates the first day of the lunisolar Tibetan calendar.
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The Jokhang monastery is more than 1,000 years old and is listed as a Unesco World Heritage Site.
The extent of the fire damage to the site, considered the spiritual heart of Tibetan Buddhism, was not known, the Post said.
Later that year, dozens of monks burst into Jokhang temple to interrupt a state-run foreign media press tour meant to showcase the region's harmony and stability in wake of the protests, accusing the government of lying.
Tibet has been ruled by China since the 1950s.