The official Xinhua News Agency cited Shanghai's municipal information office as saying three people died. A man answering the phone there confirmed the deaths and said one other crew member was seriously injured, with the other three slightly injured.
The man, surnamed Wang, said all of the crew members are foreigners but he did not know their nationalities.
China Central Television said the plane's tail struck the ground on takeoff, and an airport warehouse also caught fire in the crash on Saturday morning.
The report showed billowing thick black smoke at the scene, with police officers blocking closer access.
A reporter from Shanghai's Oriental Satellite Television told CCTV that the tail of the plane had broken in two or three parts, and hundreds of firefighters were spraying fire retardants on the plane.
The crash occurred at 7:40 a.m., Xinhua said. It said the plane, which had been headed to Bishkek, the capital of Kyrgyzstan, veered off the runway and burst into flames.
The plane was operated by Zimbabwe-based Avient Aviation, Xinhua said.
Calls to the Zimbabwe Embassy in Beijing went unanswered on Saturday morning.
CCTV said two runways at the airport were shut down. A woman answering the phone at the airport's information desk said international and domestic departing flights were delayed.
Shanghai is China's largest city and its economic capital. The Pudong airport is located on the eastern edge of the city, by the East China Sea.
In June 2008, two Chinese air force jets collided in Inner Mongolia, with both pilots parachuting to safety.
In June 2006, a Chinese military plane crashed in eastern China's Anhui province, killing all 40 people aboard.
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Eric