"I'm protesting against the recommendation to drop wrestling from the Olympics," Nazaryan, 38, was quoted as saying by the Russian wrestling federation on its website.
"Wrestling has always been part of the Olympic programme and it's not right to exclude it from the Games. I'm starting my hunger strike and from now on I will drink only syrup," said Armenia-born Nazaryan, who won gold in Greco-Roman wrestling at the 1996 Atlanta Games, competing for his native country.
He then switched his allegiance to Bulgaria, winning his second Olympic title four years later in Sydney. Nazaryan also won three world titles for Bulgaria from 2002 to 2005.
Last month, the International Olympic Committee made a surprise recommendation to drop the ancient sport from the 2020 Summer Games.
The decision has outraged the wrestling community throughout the world, prompting two former champions, Bulgaria's Valentin Yordanov and Russia's Sagid Murtazaliev, to return their Olympic gold medals back to the IOC in protest.
Part of the first modern Olympics in 1896 and all further editions, except the 1900 Paris Games, wrestling now joins seven other candidates battling for one spot in a revamped programme.
The IOC executive board will meet in St Petersburg in May to determine which of them will be put to the vote at the IOC session in Buenos Aires in September.