The entire crew was rescued. The sailors from Indonesia, Jordan and Romania were taken to the naval base in Mumbai.
The vessel was carrying a cargo of coal and was traveling from Indonesia to the western Indian state of Gujarat.
Indian navy spokesman Capt. Manohar Nambiar said that the MV Rak sent out a distress signal early Thursday morning. The navy and coast guard immediately began rescue operations.
The Coast Guard sent rescue boats and helicopters to transfer the 30 crew members of the Rak onto another vessel. The Indian navy also sent a ship to help out.
Some people who had jumped off the ship into the sea in a panic had also been saved.
30 crew members were saved from a sinking merchant ship off Mumbai's coast hours after it sent a distress signal.