The men, 36 and 32 years of age, were found busking for money on the streets, which is considered a form of begging in Thailand, The Thaiger, a news and information portal, reported.
Thai police said the Russians held a cardboard sign with the following message written in Thai and English: "Help! I am fleeing war in Russia. My money has run out. I do not want to return to the war. Can you help by donating? Do you have any free food for me?"
At a local police station, the men told the police that they entered Thailand on December 9 and that they had run out of money.
Thailand has received an influx of Russian visitors, with data showing monthly arrivals doubling in November and up nearly seven times from September, Reuters reported.
This winter, Thailand is granting 45-day stays for tourists from Russia in an effort to revive its long-furloughed tourism industry.
Foreign beggars have stirred debate in Thailand and other Asian countries over whether they deserve special support or if they are just taking advantage of their hosts to enjoy a free vacation.
In November, two European tourists were found selling jewelry on the streets of Bangkok "to fund their world tour."