Shockingly, the collapse occurred when the victims were standing on the dilapidated bridge watching an operation to rescue a youth who allegedly jumped into the river to commit suicide.
The bridge constructed during Portuguese-era across the river Sanvordem, a tributary of river Zuari, was closed for traffic for the last four years.
The incident occurred when fire and emergency services personnel were busy rescuing the youth, some 50 people were watching their efforts from the bridge when it gave way and they fell into the water.
The police said around 20 of them swam and were able to save their lives. Another 14 people were rescued and taken to nearby hospitals, whereas two bodies were retrieved from the river.
As per police officials, more people are feared to have been trapped under the collapsed portion of the bridge.
Divers from the Indian Navy and the Drishti Lifeguard Services, a private agency which provides lifeguards for the state's beaches, were called in for the rescue operation.
Chief Minister Manohar Parrikar told reporters that all concerned agencies have been pressed into action.
"A massive search and rescue operation is being carried out. We still don't have exact number of people who could be in the water," he said.
Meanwhile, Union Home Minister Rajnath Singh said he spoke to Parrikar following the bridge collapse reports.
"Spoke to Goa CM ... regarding the bridge collapse on Sanvordem river. Search and rescue operations have been intensified," Singh tweeted.