There were over 50 people standing on the dilapidated bridge when it caved in near Curchorem village.
The people had gathered on the bridge to watch the rescue operation of a youth, who had jumped into the river to commit suicide, the police said.
"While the rescue teams have recovered two bodies from the river so far, at least 30 people are still missing. Some of those who fell into the river, managed to swim ashore," the police said.
"Around 50 people had gathered on the bridge to see the rescue operation. When the bridged caved in, all of them were flung into the river. However, some of them managed to swim to the shore," the official said.
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The Indian Navy has been requested to assist in the rescue operations and the divers have rushed to the spot. The fire and emergency services has begun the search operation.
Meanwhile, Union Home Minister Rajnath Singh spoke to Goa Chief Minister Manohar Parrikar over the bridge collapse incident.
Further details are awaited.