The flight will be carried out by Thai Air International from U-Tapao airport some 140 km (90 miles) southeast of Bangkok to Moscow's Domodedovo airport, the embassy said.
Protesters from the People's Alliance for Democracy (PAD) took over Suvarnabhumi International Airport, which handles around 40 million passengers a year, on Tuesday night, blocking access and paralyzing operations as part of a long-running campaign to oust Prime Minister Somchai Wongsawat.
PAD leader Sondhi Limthongkhul was cited by the Nation newspaper as saying on Tuesday night that, "We have tried to pressure the government for more than 50 hours but nothing has happened, so we need to step up our campaign by closing the airport to tell the world about the problems Thailand is facing."
Around 700 flights were cancelled leaving 3,000 passengers stranded at Bangkok's main international airport on Wednesday.
The anti-government protests have gathered strength since early October, when a number of PAD members, who were trying to prevent an address by the new prime minister, were killed and injured during demonstrations.
The country's army chief, Anupong Paochinda, said the military were willing to help maintain public order in the country, but ruled out a coup, saying that, "Every commander in the armed forces has agreed that a coup is not the right way to resolve the current predicament."
A handful of flights have been diverted to Bangkok's Don Muang airport and a military airbase, some 190 km (118 miles) east of the capital, as well as to other Southeast Asian countries. In addition a number of airlines, including Cathay Pacific, Singapore Airlines, Malaysia and AirAsia, have canceled flights to Bangkok.