Officials said though only eight bodies have so far been recovered, more may have died in the accident that occured in Daman about 200 kms from Mumbai.
"We have so far pulled out eight bodies and all of them are children," Vishal Tandel, a senior official said.
Tandel said a school bus was among several vehicles that fell into the water after the bridge across an inlet collapsed around noon.
Officials said six people together with several motorcyclists, had been pulled out.
Eye-witnesses said the bridge collapsed suddenly.
"I heard a loud crack and saw people rushing towards me screaming the bridge is falling," Salim Anwar, a local resident, said.
"I could hear cries of help, help and I saw these rickshaws and the bus falling into the water. It was a terrible scene," he recounted.
Thursday's accident was the third big disaster to hit western India in the past week.
Earlier on Monday, two car bombs had exploded in the city of Mumbai, killing 52 people and injuring more than 120 people.
On Wednesday, a stampede at a Hindu religious festival in the town of Nashik left nearly 40 dead.