Chow Mei-ching, wife of President Ma Ying-jeou, was to leave Sunday for Monday's opening of the exhibition, at which hundreds of artefacts and artworks from the Taipei National Palace Museum would have gone on display in Japan for the first time.
The Taipei museum has said the Tokyo National Museum guaranteed in a contract that the lender's full name would be used and that the word "national" would not be omitted in promotional posters and tickets.
But less than a week before the opening, the Taipei museum said the Tokyo museum had failed to use the word "national" on many of its posters and tickets.
The name issue has long been a sensitive topic for Taiwan, which is recognised by only 22 countries after a decades-old diplomatic tug-of-war with China from which it split in 1949.
On Friday Ma's spokeswoman Ma Wei-kuo warned in a strongly-worded statement that "national dignity definitely comes before cultural exchanges".
The spokeswoman confirmed to AFP Sunday that the first lady's trip was postponed but would not provide details.
The Taipei museum said Sunday its Tokyo counterpart had shown "sincerity" by taking down the problematic posters and other measures.
But the question of whether the exhibition would open as scheduled "would be dictated by the outcome of the improvement".
Japan, like most countries, has diplomatic ties with Beijing rather than Taipei.
But it maintains close trade and other ties with Taiwan, which was its colony from 1895 to 1945.
The National Palace Museum last year announced the loan of 231 artefacts to Japan, its first to an Asian country, following exhibitions in the United States, France, Germany and Austria.
The Taipei museum boasts more than 600,000 artefacts spanning 7,000 years of Chinese history from the prehistoric Neolithic period to the end of the Qing Dynasty.
The museum's contents -- one of the world's finest collections of Chinese treasures -- mostly came from Beijing's Forbidden City. They were brought to the island by Nationalist leader Chiang Kai-shek, when he fled to Taiwan after losing the Chinese civil war to the communists in 1949.
For years the National Palace Museum was unwilling to lend the artefacts to Japan for fear that China would try to reclaim them, until the Japanese government passed a law in 2011 to prevent such seizures.
China regards Taiwan as part of its territory awaiting reunification, by force if necessary, although tensions have eased markedly since Taiwan's Beijing-friendly Ma took office in 2008.