The blaze at the restaurant, La Maison du Bois, a wooden chalet 1,800 metres up in the French Alps near the Swiss border, is thought to have started in the kitchen.
Authorities said it then spread rapidly to the dining area, where several pieces of antique furniture were destroyed.
"This is a life and a piece of French cultural history that has just gone up in flames," said Veyrat, adding "It's not just a restaurant but also a museum of popular art showing several pieces of furniture from the region. It's sad, but I'm a fighter. I'll be back".
Known as much for roaming the countryside seeking wild herbs for his dishes as for his trademark black hat, Veyrat has already once suffered a forced break in his career.
In 2009, he stopped work, saying he could no longer bear the physical strain of working in the kitchen after a serious ski accident.
He handed back the six Michelin stars he had won (for two separate three-star restaurants) and only resumed work as a chef in 2013 opening his Alpine restaurant.
Specialising in traditional dishes, with lots of wild herbs and a little "molecular gastronomy" his creations do not come cheap.
According to his website, the top 12-course tasting menu at La Maison du Bois costs 325 euros.