The goal is to spend three years in orbit around Phobos, the larger of Mars' two moons, and bring back at least 10 grams of samples from its surface.
If all goes well, the spacecraft will arrive at its destination in August next year.
The expedition is being carried out by the Japanese space agency JAXA in collaboration with American and European counterparts, as well as several universities and technology companies.
The aim is to shed light on how Mars got its moons. One hypothesis is that they formed when Mars collided with another celestial body; another is that they were asteroids captured by the planet's gravity.
Researchers also want to investigate whether Phobos could be used as a "natural space station" for future trips to Mars.