Vladimir Katriuk was second on a most wanted list compiled by the Simon Wiesenthal Center, a US organisation which investigates Nazi war criminals.
Mr Katriuk passed away aged 93 after a long illness, his lawyer said.
His death came just hours after the Centre for Israel and Jewish Affairs said Canada should ensure he was held accountable for alleged war crimes.
Russia charged Mr Katriuk earlier this month and issued a request for him to be deported from Canada to Moscow to face trial.
Russia's investigative committee alleged he took part in a 1943 massacre in the village of Khatyn, which was then in the Soviet Union and is now part of Belarus.
It is thought that all 156 residents of the village were killed by a Nazi battalion made up largely of Ukrainians soldiers.
Mr Katriuk denied any involvement in the massacre, but a 2012 study by Sweden's Lund University said that he was a key participant.
A witness told the authors of the study that he lay in wait outside a barn that had been set on fire and shot anyone who attempted to escape.
Mr Katriuk allegedly deserted from his SS unit in 1944. Court documents show he lived in Paris before emigrating to Canada in 1951.
He later became a Canadian citizen and lived with his French-born wife in Ontario, working as a bee-keeper.
Canadian authorities investigated Mr Katriuk but decided not to revoke his citizenship after failing to find evidence of atrocities.
A Ukrainian man suspected of being a Nazi war criminal has died in Canada.