The imposing fortress-monastery, which stood 4,430 feet above sea level at the confluence of two rivers, was built by the south Asian nation's founder, Zhabdrung Ngawang Namgyal, and was one of several dzongs designed to help take control of and unify the country, CNN reported.
There were no reports of injuries or deaths as a result of the fire.
The dzong housed temples as well as the seat of the administration for the Wangdue Phodrang district.
Home Minister Minjur Dorji said hundreds of the dzong's sacred relics, most of those housed there, were saved with help from the Bhutan armed forces. Many of the relics dated to the sixth and seventh centuries.
"The entire society has solidarity for the loss of one of the most important and oldest fortresses in our country," Dorji told CNN.
In a message posted on the Web site of Kuensel of Bhutan, Thinley noted another dzong, Paro Taktsang, was rebuilt after a fire in 1998.
"We must seize the opportunity to build a stronger, more durable and glorious dzong in the name of Zhabdrung Ngawang Namgyal and by the will of his majesty, the king," Thinley said.
The fire was under investigation. It was believed to have been caused by a short circuit in wiring, Dorji said.