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CCTV footage posted on social media appears to show the moment the structure collapses, hitting passers-by, auto rickshaws and nearby buildings.
Witnesses say other cars, buses and lorries have also been hit. People are said to have been living in makeshift homes under the flyover.
The army and national disaster agency in India have joined the rescue operation, which has been hampered by difficulties in getting ambulances and other vehicles close to the site.
At least 70 injured have been taken to hospitals, officials say.
Emergency teams have been sent with sniffer dogs, concrete cutters, drilling machines and sensors to detect life, a rescue official told AFP news agency.
Ramesh Kejriwal, an eyewitness, told Reuters: "There was a loud sound which scared us. The concrete had been laid last night at this part of the bridge."
Chaotic scenes: Rahul Tandon, BBC News, in Kolkata
These are chaotic scenes, as officials are desperately trying to clear the area, worried that the rest of the flyover may collapse. They are trying to bring in equipment to clear the rubble and rescue those who may be under it. But the proximity of the buildings may limit the access for heavy lifting equipment to the area.
It is a race against time and the death toll may rise. A rescue official said there were buses trapped.
Locals have been digging through the huge slabs of rubble with pick axes while police hold back relatives desperate for news of the missing.
As the operation continues, angry relatives arrive looking for their loved ones. At the same time, more bodies are being taken away.
Another eyewitness, Ravindra Kumar Gupta, told the news agency that two buses carrying more than 100 passengers had been trapped.
"Every night, hundreds of labourers would build the flyover and they would cook and sleep near the site by day," said Mr Gupta, who together with friends pulled out six bodies.
India's Prime Minister Narendra Modi, who is in Washington in an official visit, tweeted that he was "shocked and saddened" by the collapse.
"My thoughts are with the families of those who lost their lives in Kolkata. May the injured recover at the earliest," he added.
A recurring tragedy
August 2015: At least 11 people die after a building collapses near India's western city of Mumbai
July 2015: Five killed after a four-storey building collapses in Delhi
April 2013: 74 people die after a high-rise residential building in Mumbai collapses
June 2014: At least 10 people killed when a three-storey building in Delhi collapses
June 2014: At least 60 people killed when a building collapses in a Chennai suburb
November 2010: 69 killed and more than 80 injured in a collapse in Delhi
September 2009: Chimney of a power plant in Chhattisgarh caves in, killing 40 people