The bridge, built more than seven decades ago in Mahad town, crashed around 1 am after flood waters rushed into the river Savitri.
Buses and private cars are believed to have plunged into the flooded river with dozens of people after the bridge collapsed.
Two state transport buses with 11 passengers each are missing. The buses started from Mumbai but did not arrive at their destination.
Around 80 rescuers and divers have been sent to the spot, said the National Disaster Response Force.
A Chetak helicopter has been launched by the Coast Guard to help search for the missing vehicles.
Prime Minister Narendra Modi has spoken to Maharashtra Chief Minister Devendra Fadnavis and assured all help in rescue and relief ops.
“There were two parallel bridges. One is a new bridge and one constructed during the British era. The old one collapsed,” tweeted Mr Fadnavis late last night.
The chief minister also said there is “no confirmed assessment about casualties since the area is very dark.”
Traffic has been diverted to the new parallel bridge. Officials are trying to determine whether more vehicles are missing.
For five days, there has been incessant rain in parts of coastal Konkan, northern and western Maharashtra.
Over 20 people are reported missing after a British-era bridge collapsed on the Mumbai-Goa highway in Maharashtra late last night because of heavy rain. Two buses and several vehicles plunged into the river near Raigad district, 84 km from Mumbai.