The men were held in the city of Perm, some 1,400km (870 miles) east of Moscow, local investigators said.
Their statement said that the suspects had targeted the 25-year-old victim out of "personal hostility".
It was not clear when the incident occurred. The men - who have not been named - have been charged with murder.
The investigators said on Friday that the body of the man had been found in a forested area near a public transport stop in Perm.
They said the three men attacked their victim with knives and a hammer.
"After carrying out the attack, the corpse was dismembered. Part of it was eaten and part was also sold to a kebab and pie kiosk," their statement said.
It was not immediately clear if any customers had been served.