The H-2B rocket blasted off from the southern island of Tanegashima at 04:48 am local time (1948 GMT Saturday), images broadcast by the Japan Aerospace Exploration Agency (JAXA) showed.
According to JAXA the first few minutes of flight had gone to plan.
The unmanned rocket carried a cargo transporter filled with drinking water, food, clothing and work supplies for the six permanent ISS crew.
The annual mission, which has previously been completed by countries including the United States and Russia, will also pick up waste from the space centre.
Standing at just 34 centimetres tall and weighing about one kilogram, Kirobo is programmed to communicate in Japanese and keep records of its conversations with Wakata, who is the first Japanese astronaut to command the ISS.
"Kirobo will remember Mr Wakata's face so it can recognise him when they reunite up in space," its creator Tomotaka Takahashi told AFP in June. "He will be the first robot to visit the space station."
Sending the android to space is part of a study aimed at seeing how a non-human companion can provide emotional support for people isolated over long periods.
Back on earth, twin robot Mirata will be on the lookout for any problems encountered by its electronic counterpart, which was inspired by the legendary animation character Astro Boy.
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