Unconfirmed sources have put the death toll at 24.
The police said that 21 persons died in the incident in Burrabazar area, which houses the city's largest wholesale market, while at least 88 others were injured.
Fifteen of the dead were identified while the identification process of the rest were on, police said.
The injured were rushed to hospitals in the vicinity.
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West Bengal Chief Minister Mamata Banerjee, camping at the site, said "it is not the time to play politics. Rather we should work for the rescue and relief of the injured."
Banerjee later visited Calcutta Medical College and Hospital and inquired about the condition of the injured.
She said 17 injured were being treated at the hospital while the rest had been discharged. Of the 17, condition of two were critical, while three bodies were still trapped in the debris and would have to be extricated with the help of gas cutters, she said
In a related development, Kolkata Police registered a case against the Hyderabad-based construction firm IVRCL under sections 304, 308 and 407 of the IPC and sealed the local office of company engaged in the flyover's construction.
"It is nothing but God's act," claimed Panduranga Rao of IVRCL, drawing all-round flak.
Chief Secretary Basudeb Banerjee said that a high level inquiry has been ordered into the flyover collapse.
Meanwhile city police Commissioner Rajeev Kumar handed over a report about the incident to the Chief Minister.
West Bengal Governor K N Tripathi, who visited the spot, sought a report of the incident from the state government.