Many people are feared trapped under the concrete and steel bridge, which fell on a busy road.
Fist images from the site showed residents using their bare hands to help the rescue effort.
Construction projects in India have often suffered from safety issues with frequent collapses.
According to experts, 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 reported.
Emergency teams have been sent to the area near Girish Park, but witnesses say there is little sign of co-ordinated rescue efforts.
The collapsed structure appears to have hit cars, trucks and nearby shops.
The accident took place in one of Kolkata’s most densely populated neighborhoods, with narrow lanes, and shops and houses built close together.
The proximity of the buildings may limit the access for heavy lifting equipment to the area.
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