The rocket lifted off into an overcast sky from the southern island of Tanegashima on schedule at 11:06 am (0206 GMT), according to live images relayed by the Japan Aerospace Exploration Agency (JAXA).
About 15 minutes later, the rocket released a cargo vessel called "konotori" (stork in Japanese), containing supplies such as food, clothing and tools necessary for experiments to be done in space.
JAXA officials declared the launch a success and were scheduled to address the media later.
The cargo should reach the International Space Station, where Japanese astronaut Akihiko Hoshide is staying, on July 27.