"The bus was travelling from Goa to Mumbai when the driver suddenly lost control," an officer in the police control room told AFP.
The pre-dawn accident happened in the Khed area of Ratnagiri district, around 350 kilometres (220 miles) south of the state capital Mumbai.
Most of the injured, including the driver, sustained head and arm injuries and were undergoing treatment at a local hospital, said the officer.
Images from the scene showed the bus lying on its roof next to a bridge. The vehicle had landed on a dried-up patch of land next to low-lying water.
Media reports said there were some foreign tourists on the bus, but there was no immediate confirmation from the police.
About 110,000 people were killed in Indian road accidents in 2011 -- more than 300 every day -- according to the last available statistics from the National Crime Records Bureau.
Bad roads, speeding vehicles and poor driving were among the contributing factors, and bus crashes with a double-digit death toll are far from rare.
Tuesday's crash came a day after a senior official revealed that more than 800 people have died in accidents on the Mumbai-Goa highway in the last three years.
Maharashtra's home minister R R Patil, in a written reply to a question, told the state legislature Monday that 828 people died and 2,411 were seriously injured between 2010 and the end of 2012, the Press Trust of India reported.
The World Health Organization's global status report on road safety 2013 found that eight percent of India's road user deaths were drivers or passengers of buses, while 32 percent were riders of motorbikes or three-wheelers.
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