BTS apologised in a statement to its Japanese fans for not being able to make the appearance, without elaborating.
The "atomic bomb" T-shirt also featured Korean independence slogans.
The t-shirt appeared to reference the end of the Japanese occupation of Korea, which ended in 1945 after the USA dropped two atomic bombs on the Japanese cities of Hiroshima and Nagasaki.
The seven-member boy band was scheduled to appear on TV Asahi's flagship music program, Music Station, Friday night. The network said it talked to the record label about the shirt and then made a decision to cancel the appearance.More news: Oil tanker rams into Norwegian frigate, leaving eight injured
Many have pointed out that while the controversy over the t-shirt design has been mentioned, another reason for the postponement may be the increasingly deteriorating relations between Japan and South Korea.
Hundreds of thousands of people were killed instantly and many more died in the years to come as a result of radiation sickness.
Jimin, 23, was reportedly photographed wearing the shirt previous year on 15 August, when Koreans mark the anniversary of the end of the Japanese occupation.
Both South Korea and Japan are particularly sensitive when it comes to the legacy of World War II. Despite IZ*ONE's successful debut stage on KBS's ' Music Bank' last week, some netizens are still petitioning the girl group's promotions on the station; the government petition demanding a ban on IZ*ONE from appearing on public broadcast station programs now has approximately 30,000 signatures.More news: 'Heartbreaking', 'Gutted' - Some Fans React After Arsenal Star Suffers Serious Injury
But other fans rallied around BTS. "Jimin don't blame yourself", said one Twitter user.
Agreeing comments included, "I suddenly don't want to see IZ*ONE's faces", "Can't stand Mnet and CJ right now, just look at what they're doing", "That's messed up", "Mnet has got to feel at least some guilt right now", "Sorry IZ*ONE, I didn't really dislike you guys or anything before but now this is making me angry", "Can they just please ban IZ*ONE from KBS", etc.
Earlier this week, a South Korean court ordered a Japanese company to compensate them for wartime labour during Japan's colonial rule of the Korean peninsula. With the Japanese government maintaining that all matters of compensation were settled through a treaty in 1965, political tension is high between the two countries.More news: Dead After California Shooting At Popular Nightspot, Police Say