The seven-member boy band, who have built a huge international following since they formed in 2013, were due to appear on TV Asahis flagship Music Station show on Friday evening.
But the broadcaster withdrew its invitation this week after a photo of Jimin wearing the T-shirt went viral.
I can never accept the act that #BTS member wore the atomic bomb T-shirts humanely. The problem is not the relation between Japan and Korea. Its just humanity. pic.twitter.com/x37nZs8pJG
The back of the shirt features several lines repeating the words Patriotism ourhistory (sic) Liberation Korea, a reference to the end of Japans 35-year colonial rule of the Korean peninsula.
It also carries images of what appears to be a mushroom cloud created by an exploding atomic bomb, and of Koreans celebrating their liberation from Japanese rule in August 1945, the month the US carried out nuclear attacks on Hiroshima and Nagasaki.
Jimin, 23, was reportedly photographed wearing the shirt last year on 15 August, when Koreans mark the anniversary of the end of the Japanese occupation.
We have seen news that a T-shirt worn by one of the members has set off a furore. After asking their record company about this, we made the decision to postpone their appearance on our Nov 9 show, TV Asahi said.
BTS apologised for the cancellation but made no reference to the T-shirt. We apologise for disappointing fans who were looking forward to this. BTS will continue their efforts to connect with fans on stage and also through music, the group said.
The row comes amid a sharp deterioration in ties between Seoul and Tokyo that began when South Korea suggested it would revisit a 2015 agreement over Japans prewar and wartime use of tens of thousands of sex slaves, most of whom were from the Korean peninsula.
Japan then withdrew from an international naval review in South Korea after Seoul demanded that it remove the rising sun ensign from its warship. Many South Koreans regard the flag as a symbol of Japanese militarism and colonial rule.
Last month, the South Korean supreme court ordered a Japanese company to compensate four South Koreans it had used as forced wartime labour – a decision the Japanese government has called unacceptable.
The cancellation of the bands TV appearance comes on the eve of their Japan tour, which begins in Tokyo next Tuesday, and five months after they became the first K-pop band to top the Billboard 200 album chart with Love Yourself: Tear. This week their ninth single in Japan, Fake Love/Airplane pt 2, topped the countrys Oricon daily singles chart.
The band, who are also known as the Bangtan Boys, performed in Paris last month in front of the South Korean president, Moon Jae-in, with whom they later posed for photos. They have also played to huge audiences in London and New York.
K-pop group BTS have caused controversy after a band member wore shirt depicting the US atomic bombing of Japan.