In a pre-dawn raid prompted by a tip-off, the military police found "tens of kilograms of matter that appears to be a psychoactive substance" inside Jadran, a sailing ship which was moored in the Adriatic port of Tivat, the ministry said.
Montenegrin navy divers have also searched the hull of the ship, it said in a statement.
The Podgorica-based daily Vijesti said authorities had seized as much as 50 kilograms of cocaine on board the vessel but that no arrests had been made.
Teachers and students of Montenegro's Naval Faculty were not on board the vessel during the raid, the ministry said. They were expected to board the ship later and depart on a training cruise.
"Operatives of the police department and the military police ... are taking steps to uncover the culprits," the ministry said in a statement.
Jadran, once the main training ship of the now-defunct Yugoslav Naval Academy, was taken over by Montenegro's navy after the country declared independence from Belgrade in 2006. It is used solely for training purposes.Montenegro, a member of NATO, also aspires to join the European Union but it must first do more to tackle organised crime and corruption and to improve the rule of law.