The H2-A rocket was also carrying a research satellite developed with NASA and the European Space Agency.
It was meant to launch from Japan Aerospace Exploration Agency (JAXA)'s Tanegashima Space Center in southern Japan at 9:26 a.m. local time (0026 GMT) on Monday.
Japan has yet to set a new date for the next attempt.
Latest lunar mission attempt
Japan had attempted last year to launch a lunar mission named Omotenashi, which was carried on NASA's Artemis 1. The mission was nevertheless unsuccessful after communications were lost.
In April this year, Japanese start-up ispace also took a chance to become the first private company to land on the moon, yet it also failed.
JAXA aims to land the "Moon Sniper" within 100 meters (330 feet) of a specific target on the moon. This is far less than the normal range of several kilometers.
Last week, India's low-cost space program succeeded in landing a mission near the moon's south pole. Only the United States, Russia and China had previously managed to place a spacecraft on the lunar surface. None had managed to do that on the moon's south pole.