One vessel, which was carrying a cargo of diesel and lubricant oil, tilted dangerously after the collision between the two Panamanian ships five nautical miles from the shore, triggering an oil slick.
Environmental emergency teams have been put on alert to mobilise for a clean-up operation, while fishermen have been told not to venture into the sea until the all-clear has been given.
Broken patches of oil have been cleared around Elephanta Island, a world heritage site and tourist attraction in Mumbai Harbour, the defence ministry said in a statement.
The MSC Chitra was leaving Mumbai when it collided with the MV Khalijia-II, which was manoeuvring into port.
Thirty-three crew members were rescued. Both ships developed cracks following the collision.