The incident took place at 4:30 AM in the morning when there was hardly any traffic on the Ultadanga flyover, which connects VIP Road and the airport with E M Bypass and the eastern and southern suburbs.
As the debris fell into a canal running below the flyover, it took down a truck, police said.
The driver and two others were rescued from the canal by fire-brigade personnel and locals, they said.
Disaster Management personnel and police were searching for victims, if any, in the rubble and canal.
Urban Development Minister Firhad Hakim, who rushed to the spot, said a crack was detected in the flyover one-and-a-half years ago and examined by experts of Jadavpur University.
The problem detected then was not related to maintenance but a technical fault in the bolt system, he said.
The flyover was built two years ago during the earlier Left Front government.
Mr Hakim said that action will be taken against engineers found responsible for today's collapse and a third party inspection of the entire flyover will be made.
Cranes will be used to clear the debris of the flyover from the canal known as Keshtopur Khal, he added.
"This flyover was built in a hurry so that it could be inaugurated by then chief minister Buddhadeb Bhattacharjee before the 2011 assembly elections," Mr Hakim alleged.
Though the flyover was properly maintained, he said, the problem was in its faulty construction.
However, his predecessor in the Left Front government, Ashok Bhattacharya, trashed Hakim's contention that the faulty construction was to be blamed for today's collapse.
"The flyover was constructed in 2009-10 and no problem was detected subsequently. How can it be said that there were faults in the construction?" he asked.
Mr Bhattacharya said most flyovers in the city were built during the Left Front regime and there was no problem with any of them.
"There is no point in blaming the Left Front government. They should make a proper inquiry to see if the flyover was properly maintained," he added.