Additional police director-general P. Chandrasekharan told media that the passports of crew members on the Italian vessel Enrica Lexie had been impounded by authorities in the southern Indian state of Kerala.
"Police have registered a case of murder against the crew members and later names can be added or delisted," he told AFP of the probe underway into the shooting on Wednesday 64 kilometres (40 miles) off the coast of Kerala.
"The crew will not be allowed to leave the port until the finalisation of legal procedures," Chandrasekharan added.
The 58,000-tonne vessel, which was ordered to anchor seven kilometres off Kerala's Cochin city, sailed into the harbour late on Thursday night, Indian navy spokesman Roy Francis said.
The tanker carrying crude oil was on its way from Singapore to Egypt when the incident occurred, Francis added.
The Italian navy in a statement said on Thursday the Indian fishing boat had behaved aggressively and had been warned on several occasions by the naval officers on board the Enrica Lexie.
Local officials say the motorised fishing boat with 11 men had sailed out to trawl for tuna fish on February 7 and was homebound when it was fired upon.
Shipping companies are increasingly employing security guards to protect their vessels because of dangers in the seas off the coast of Somalia where ships of all sizes have been seized by pirates.