Japan's government asked on Wednesday for all sports and cultural events in the country to be scrapped or curtailed for the next two weeks due to the outbreak.
Sunwolves chief executive Yuji Watase told reporters in Japan that the Crusaders' match won't be held in the country.
"We are trying to relocate the Brumbies' match on 8th March in Osaka and the Crusaders' match on March 14th in Tokyo to overseas," he said.
"In the beginning, we tried to hold these matches in Japan behind closed doors, but when we thought about what is the best solution, we came to the conclusion to hold these games abroad."
SANZAAR yesterday announced next Friday's match between the Sunwolves and Brumbies in Osaka had also been postponed and future fixtures were being talked about.
"Advanced discussions have been held to adequately address this recent announcement by the Japanese government," the organisation said.
"SANZAAR is now working to determine if this match can be relocated. SANZAAR will issue further details on the position of this match and any potential further disruptions in the near future."
The Sunwolves play their home games in Japan and Singapore but are currently in New Zealand for a match against the Hurricanes in Napier on Saturday.
No-one involved with the Sunwolves had tested positive for the flu-like virus, SANZAAR said. Players and officials with the team are undergoing daily testing.
The potential cancellation or relocation of the game from Osaka would be the first Super Rugby match to be affected by the virus, although the Ireland-Italy Six Nations clash in Dublin on March 7 was postponed on Wednesday due to an outbreak in northern Italy.
The Hong Kong and Singapore legs of the Sevens World Series, originally scheduled for April, were last month also postponed until October to curtail the spread of the virus.
The virus originated in China late last year and has infected about 80,000 people worldwide and resulted in more than 2,700 deaths, mostly in mainland China.
It has already forced the cancellation, postponement or relocation of several other sporting events in Asia, including the world indoor athletics championships that were scheduled for Nanjing from March 13-15.