The H-IIA rocket blasted off from Tanegashima Space Center in the south of the country at 1:22 pm (0422 GMT) after delays due to bad weather.
The Japan Aerospace Exploration Agency (JAXA) sent the probe, Hayabusa2, on a six-year mission.
The USD 260-million project will send the explorer towards the 1999JU3 asteroid in deep space.
It will blast a crater in the asteroid to collect materials unexposed to millennia of wind and radiation, in the hope of answering some fundamental questions about life and the universe.
It will also study the surface by dropping tiny robots. If all goes well, asteroid samples will be returned to Earth in late 2020.