In a statement Monday, NATO says the Danish warship Absalon intercepted and scuttled the ship on Sunday, just hours after the vessel left a "well-known pirate camp" on the eastern Somali coast.
It says the sunken vessel was a mothership, a large boat from which pirates launch attacks on commercial shipping. There was no word on what happened to the pirates on the ship.
NATO says it expects pirate attacks to increase with the end of a regional monsoon season but that both NATO and European Union anti-piracy forces are positioned to stop pirates as they head out to sea.
The Absalon is the flagship of NATO's anti-piracy force off the Horn of Africa.
Somali pirates have made tens of millions of dollars over the past two years hijacking ships for ransom.
The NATO alliance says one of its warships has sunk a Somali pirate vessel in the Indian Ocean.