An uncrewed rocket carrying the Chang'e-6 probe blasted off from the Wenchang Space Launch Center at about 17:27 local time (10:27 BST).
The 53-day mission aims to bring around two kilograms of lunar samples to Earth for analysis.
It will try to relaunch from the side of the moon facing away from Earth.
This is sometimes described as the dark side of the Moon because it can't be seen from Earth, not because it does not catch the sun's rays.
It has a thicker, older crust with more craters, which are less covered by ancient lava flows than the near side.
Scientists hope this may make it easier to collect material that could shed light on how the Moon was formed.
Ge Ping, vice director of China's Lunar Exploration and Space Engineering Center, told reporters ahead of the launch: "Chang'e-6 will collect samples from the far side of the Moon for the first time."
The probe was named after the Moon goddess and one of the most popular figures in Chinese mythology.
It is expected to make a soft landing in the South Pole-Aitken Basin, a vast depression which is 2,500km (1,553 miles) wide and up to 8km (5 miles) deep.
It then aims to collect lunar soil and rocks, and conduct experiments, using a drill and a mechanical arm, the China National Space Administration said.
It will use a relay satellite named Queqiao 2 to communicate with the Earth, it added.
The launch marks the first of three uncrewed missions to the moon planned by China this decade.
Chang'e-7 will search the lunar south pole for water, and Chang'e-8 will attempt to establish the technical feasibility of building a planned base, known as the International Lunar Research Station.
Its predecessor, Chang'e-5, retrieved the youngest ever lavas from the Moon on its return in December 2020.
Friday's lift off marks the latest stage in China's space exploration programme that is competing with the US.
Five years ago China became the first country to land a rover on the Moon's far side.
By 2030, it aims to have put its first astronauts on the Moon, and to have sent probes to collect samples from Mars and Jupiter.
By Jemma Crew