The victim, who owns large meat-processing plants, was in a sauna with his wife when the attack happened, the Investigative Committee said.
The committee did not name the man — but state media identified him as Vladimir Marugov, citing his ex-wife Tatyana Marugova, who confirmed his death.
“Several masked men entered the bathhouse … tied up the owner of the house and his spouse, and then demanded money,” the Investigative Committee’s statement said.
Marugov’s wife managed to escape through a window and call police, who found her husband dead at the scene along with the crossbow used to shoot him, investigators said.
The Investigative Committee has launched a criminal investigation, according to the statement published on its official website.
Late Monday, state-run news agency RIA Novosti reported that one suspect had been detained for questioning.