The Japan Football Association (JFA) had hoped to host the March 25 match in Shizuoka, and New Zealand in Tokyo four days later, to "rally the nation".
The match against Montenegro should have been a celebratory occasion with the Blue Samurai playing their first match at home since winning a record fourth Asian Cup in January.
But with fire breaking out at a crippled Japanese nuclear plant and low levels of radiation wafting into Tokyo, JFA chief Junji Ogura decided to cancel the match in the city southwest of the capital, the Kyodo news agency reported
The JFA will, however, play a match on March 29 against a domestic side if New Zealand, who are due to make a decision on whether to compete on Thursday, opt against travelling.
"We have decided to hold a charity match at Nagai Stadium on March 29," the Kyodo news agency reported Ogura as saying.
"Details still need to be sorted out but we hope to play New Zealand, which like Japan has also suffered damage from a big earthquake," Ogura said, referring to the 6.3 magnitude earthquake that struck Christchurch last month killing at least 166 people.
"Coach (Alberto) Zaccheroni and the Japan national team players have said they want to do something to help the victims of this disaster."
Japan captain Makoto Hasebe echoed the need to use the game to give some cheer to the suffering people.
"Japan is facing a very tough time right now and we very much want to give the people something back in return, however small," Hasebe said.
New Zealand football chiefs said earlier on Wednesday that they wanted to compete but had to make sure it was safe to travel to Japan.
"There's a huge desire to show solidarity with the Japanese people but we need to be able to guarantee the safety of our players and staff, as would any responsible organisation," New Zealand Football chairman Frank van Hattum said.
"We are currently working with the Japanese FA and the appropriate government authorities to confirm whether those guarantees can be provided."
Japanese football officials had already postponed the domestic J.League indefinitely with most of the sporting calendar in the country also on hold.
