The injured were rushed to SSKM and CMRI hospitals.
Ms Banerjee said she has been monitoring the rescue operations from the hills.
A flyover under construction collapsed in crowded Burrabazar area, the wholesale business hub of the city, on March 31, 2016, claiming 26 lives.
Mamata Banerjee, chief minister of West Bengal state, confirmed that one person was killed, adding, "19 people have received injuries". The metro work allegedly caused traffic congestion and flooding, as well.
Earlier in the day, at around 4:30 PM, a portion of the arterial Majerhat bridge in the southern part of the metropolis collapsed.
Chief Minister Mamata Banerjee, who is now in Darjeeling, is expected to cut short his visit and return to Kolkata on Wednesday and visit the site.
The chief minister also announced a compensation of Rs 5 lakh to the family of the dead and Rs 50,000 each to the injured.
Urban Development Minister Firhad Hakim said on Tuesday heavy construction work as part of the Metro project next to the Majerhat bridge could have weakened its pillars.
NDRF DG Sanjay Kumar said earthmovers are being used for clearing the area.
"Since the Majerhat bridge is very old, it is hard keep track of documentation".
Going by the complaint, the police is to identify the agency that was in charge of maintenance of the busy bridge, located on the Diamond Harbour Road, and that is to be blamed for the collapse.
"There could be a few trapped underneath the collapsed bridge". The local train services were suspended from 4:45 pm, he said.
Circular Railway services and local train services in Budge Budge-Sealdah line were affected, an Eastern Railway spokesman said in Kolkata.
This is a third bridge collapse in the city since 2013. "There are no flights in the evening, we are unable to do so", Banerjee said. A tender for its surface repairing was floated in April this year by the Executive Engineer, Behala Sub Division of Public Works Department (PWD) but so far department has not gone public about it, saying that the five decade-old bridge was maintained by them. Devastating. Rescue teams, disaster management teams, Police CP, fire fighters already reach spot. "A portion of the bridge has collapsed and it is an unfortunate incident", he said.
Meanwhile, a political slugfest erupted with the Opposition parties on Wednesday accusing the TMC government of "neglecting" fix and maintenance of bridges and only painting various installations blue and white.