The single-seater aircraft's team spent more than a week waiting in Mandalay for weather conditions to improve in southwestern China for what will be one of the most challenging legs of the round-the-world attempt so far.
Speaking on a live feed from mission control in Monaco, Prince Albert gave pilot Bertrand Piccard clearance for takeoff.
"Bertrand, from Albert, you are clear to proceed," Prince Albert.
"Have a nice flight,"
"Thank you very much my friend," Piccard replied before taking off at around 3:35 am local time (2105 GMT Sunday) into the dark pre-dawn skies.
Piccard, one of the two Swiss pilots of the solar-powered plane, will have to battle extreme cold of down to minus 20 degrees Celsius in the cockpit and the general unpredictabilities of flying above the mountainous
Chinese provinces of Yunnan and Sichuan.
Flying at high altitude for most of the journey, Piccard will also need to use additional oxygen.
The 1,375-kilometre (854-mile) route is expected to take around 18 hours.
While the weather forecast in China is mainly clear, the team anticipate strong, low-level winds in Chongqing to be a challenging part of the flight.
If the plane flies direct it will cross over a remote region of Myanmar's border with China where intense fighting has broken out between predominantly ethnic Chinese Kokang rebels and Myanmar's military.
The fighting has forced tens of thousands of refugees to flood into neighbouring Yunnan province.
Earlier this month Beijing mobilised fighter jets to patrol its side of the border after a bomb, apparently from a Myanmar warplane, landed in a sugar plantation in Chinese territory, killing five.
The team behind Solar Impulse 2, which has more than 17,000 solar cells built into its wings, hopes to promote green energy with its circumnavigation attempt.
Ridiculed by the aviation industry when it was first unveiled, the venture has since been hailed around the world, including by UN chief Ban Ki-moon.
Muscat was the first of the 12 planned stops on the plane's maiden journey from Abu Dhabi, with a total flight time of around 25 days spread over five months.
From Oman the plane flew to the Indian city of Ahmedabad before heading to Varanasi and then Mandalay.
From Chongqing it will depart for the eastern coastal city of Nanjing before embarking on the most arduous leg of its journey, an 8,172-kilometre, 120-hour odyssey across the Pacific to Hawaii.