About 15 minutes later the rocket released the 5.5-tonne cargo vessel called "Kounotori" (stork in Japanese), which contains supplies including food, water, clothing and tools necessary for experiments in space.
"It was released successfully and we will check if it now can go into its scheduled orbit," said an official of Mitsubishi Heavy Industries, a launch partner.
The mission should reach the International Space Station, where Japanese astronaut Kimiya Yui is staying, on August 24.
Yui has been tasked with catching the cargo vessel with robotic arms and then affixing it to the space station.
The cargo also contains parts for a water recycling system, after the US-based National Aeronautics and Space Administration NASA asked its Japanese counterparts to include them as "emergency materials" following the failure in June to launch the US Falcon 9 rocket.
The unmanned SpaceX rocket exploded minutes after lift-off from Cape Canaveral, Florida, marking a major setback for the company headed by technology tycoon Elon Musk.
The accident was the third in less than a year involving US and Russian supply ships bound for the International Space Station, and raised new concerns about the flow of food and gear to the astronauts living in orbit.
An H-IIB rocket lifts off from the island of Tanegashima, Kagoshima Prefecture.