It was not immediately clear what cargo the ship was carrying. Press Trust of India reported that officials from the navy, coast guard, local police and intelligence agencies were searching the ship.
North Korean ships have in the past been accused of clandestinely ferrying nuclear materials, missile parts and arms.
Navy and coast guard officials were questioning the 44-member crew aboard the Hyang Ro after it anchored near Calicut, a port in southwestern India, PTI quoted Roy Frances, a naval spokesman, as saying.
"The vessel entered Indian waters without the mandatory clearances from the authorities," Frances said.
The crew members, all North Koreans, said the ship had developed "an internal leak in its tank," Frances said, adding that this claim was being investigated.
Local fishermen Friday alerted the coast guard about the presence of the ship.
The cargo ship, owned by the Pyongyang-based Sinhung Shipping Company, had sailed from Colombo, Sri Lanka, and was headed for Pakistan's Bin Qasim port near Karachi.