The Civil Aviation Administration of China said in a statement the crash occurred near the city of Wuzhou in Teng county.
The flight was travelling from Kunming in the western province of Yunnan to the industrial centre of Guangzhou along the east coast, it added.
There was no immediate word on numbers of dead and injured. The plane was carrying 123 passengers and nine crew members, the CAAC said, correcting earlier reports that 133 people had been on board.
The CAAC said it had sent a team of officials, and the Guangxi fire service said work was underway to control a mountainside blaze ignited by the crash.
Satellite data from NASA showed a massive fire just in the area of where the plane went down at the time of the crash.
Calls to China Eastern offices were not immediately answered. State media said local police first received calls from villagers alerting the crash around 2.30pm on Monday.
Shanghai-based China Eastern is one of China's top three airlines, operating scores of domestic and international routes serving 248 destinations.
The flight that crashed appeared to be Flight No. MU5735 from Kunming to Guangzhou, according to data from flight-tracking website FlightRadar24. It showed the Boeing 737-89P rapidly lost speed after 0620 GMT before entering a sharp descent.
The plane stopped transmitting data just southwest of the Chinese city of Wuzhou.
The aircraft was delivered to China Eastern from Boeing in June 2015 and had been flying for more than six years.
The twin-engine, single aisle Boeing 737 is one of the world's most popular planes for short and medium-haul flights.
China Eastern operates multiple versions of the common aircraft, including the 737-800 and the 737 Max.
The 737 Max version was grounded worldwide after two fatal crashes. China's aviation regulator cleared that plane to return to service late last year, making the country the last major market to do so.
China's last deadly crash of a civilian jetliner was in 2010.
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