The spacecraft, produced by Tokyo-based startup ispace and carrying a UAE-built rover, blasted off aboard a Falcon 9 rocket at 2:38 am (0738 GMT).
Measuring just over two by 2.5 meters, the spacecraft has a payload that includes a 10-kilogram rover built by the United Arab Emirates (UAE).
So far only the United States, Russia, and China have managed to put a robot on the lunar surface. And now UAE is the fourth country that has succeeded in landing on the moon.
The Gulf country is a newcomer to the space race but sent a probe into Mars' orbit last year. If the rover, named Rashid, successfully lands, it will be the Arab world's first Moon mission.
UAE Vice-President Sheikh Mohammed bin Rashid Al-Maktoum celebrated the launch as "part of the UAE's ambitious space program" in a tweet on Sunday.
"Our goal is to transfer knowledge, develop our capabilities, and leave a scientific footprint in human history," he said.

The UAE's Mohammed Bin Rashid Space Centre said a signal from the spacecraft had successfully been received by ground control.
The ispace, which has just 200 employees, has said it "aims to extend the sphere of human life into space and create a sustainable world by providing high-frequency, low-cost transportation services to the Moon."
A Japanese startup's spacecraft was launched to the Moon on Sunday in the country's first-ever lunar mission and the first of its kind by a private company.
The launch was carried out by Elon Musk's SpaceX at Cape Canaveral in the US state of Florida after two postponements for additional pre-flight checks.
The ispace mission is the first of a program called Hakuto-R, which means "white rabbit" in Japanese.
The company said its lunar lander was expected to touch down on the visible side of the Moon in April 2023 -- the Year of the Rabbit in the Japanese zodiac.