The vehicle hit people on a road next to the busy People's Square just before 9am, according to the government.
Witnesses quoted by local news source The Paper said it was already on fire as it drove onto the pavement and ended up outside a Starbucks cafe.
Others claimed the van was carrying gas canisters, with bystanders reportedly trying to break the van's windows to pull out six people who were inside.
Government officials said 18 people had been taken to hospital and that three were in a serious condition.
The cause of the incident is under investigation and comes as British Prime Minister Theresa May is due to speak in the city.
A Starbucks spokesman said its shop was not damaged and that customers and staff were safe.
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