A Shanghai police statement said the incident has been ruled a "traffic accident", saying it occurred when flammable materials inside the auto burst into flames, causing the van's 40-year-old driver to lose control of the vehicle.
He added that the driver seemed unconscious while two other people in the van were badly burned.
In 2013, two tourists were killed when a vehicle rammed into bystanders at Beijing's iconic Tiananmen Square before bursting into flames.
"The driver couldn't see the road ahead", he said. "People saw it and quickly tried to get away but a lot of people were still hit".
A local media outlet called The Paper initially reported that several people were inside the van and that it held several canisters of gas.
Police said the driver of the minivan is suspected in illegal transportation of flammable materials.
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A minivan jam-packed with gas canisters has ploughed into pedestrians in Shanghai.
They say he has been arrested on suspicion of risky driving and illegal transport of unsafe substances.
The other injured are also receiving medical treatment. Her schedule went ahead as planned.
The crash occurred at 9.15am when the PM was meeting the Mayor of Shanghai in the Xingguo Hotel.
Other speakers at the event included Li Shufu, the chairman of Chinese carmaker Geely, and Nobel Prize-winning physicist Kostya Novoselov.
Ms May on Thursday met Chinese President Xi Jinping in Beijing as part of her three-day visit aimed at establishing a new trading relationship after Britain leaves the EU.