Additional Director General of Police Tomin J Thachenkary, who is also heading the Kerala Coastal Police, said the ship was subsequently taken into custody.
The authorities in Kerala are waiting for the Centre's nod to initiate legal action against the captain of the ship and others responsible for the accident.
"There is a provision for arresting the ship," said Mr Thachenkary.
Kerala Fisheries Minister J Mercykutty Amma said the captain and crew could be booked under the IPC provision dealing with culpable homicide.
The injured fishermen were admitted to various hospitals in Kochi and the condition of two of them was stated to be serious, the police said.
Another occupant of the boat was missing and a search operation was on to rescue him.
The boat carrying 14 fishermen was hit by the ship at around 2 am, around 20 nautical miles off the Kochi coast. Most of the fishermen on board the boat were from Tamil Nadu and Assam, the police said. The fishing vessel, named Carmel Matha and owned by Nazaer Palluruthy, capsised immediately after it was hit by the ship.
The 11 injured persons were rescued by fishermen who were on another boat.
The rescued fishermen said their boat was hit while it was being anchored in the sea after fishing. A Cochin Port Trust official said the ship, which was taken into custody by the police, could not be berthed at the Port Trust due to its huge size.
The ship could remain in the outer anchorage position, he added.
The Navy said a search-and-rescue operation was on and an advanced light helicopter and the INS Kalpeni were pressed into service to trace the missing fisherman.
Kerala Chief Minister Pinarayi Vijayan has announced an aid of Rs 2 lakh each for the families of the deceased fishermen. It will be given from the Labour Department's Settlers Employees Welfare Scheme, he said in a statement in Thiruvananthapuram.
He also directed the police to conduct a "fruitful" probe and take necessary action against those guilty.