Many people are feared trapped under the concrete and steel bridge, which fell on a busy road.
Images showed residents using their bare hands to help the rescue effort.
Construction projects in India have often suffered from safety issues with frequent collapses.
Experts say there is a lack of inspections and substandard materials are used.
The flyover has been under construction since 2009 and has missed several deadlines for completion, Reuters news agency said.
Emergency teams have been sent to the area near Girish Park, but witnesses say there is little sign of co-ordinated rescue efforts.
India: Kolkata flyover collapses `killing at least 10`
31 March 2016
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At least 10 people have been killed and several others injured after a flyover under construction collapsed in the eastern Indian city of Kolkata (Calcutta), officials say.
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