The attackers boarded the ship - identified as the Tulun - from a vessel sailing under Cambodian flag, Russian maritime officials were quoted as saying.
South Korean and Japanese coast guards alerted the officials about the incident in the Sea of Japan, about 400 nautical miles (740 kilometres) south of the Russian port of Vladivostok.
There was no indication of who could be behind the attack.
The officials said the trawler was carrying 23 crew members.
A Russian Foreign Ministry spokesman, Alexander Yakovenko, told Russian television that the ministry had instructed its embassies in Tokyo, Seoul and other countries to "secure all available information from authorities".
The ship reportedly used by the attackers, the Korf, is listed in the Lloyd's shipping register as a Russian vessel.
According to the Interfax news agency, the Tulun is much bigger and is registered in the port of Kholmsk on the Russian island of Sakhalin.
The Russian border guards service said it was trying to pinpoint the vessel's exact location, as its satellite navigation had been switched off.
Fish poaching and piracy are reported to be common in the Sea of Japan.