It said Denmark's warship fired warning shots on Saturday, forcing the vessel to stop and its crew to surrender.
Sixteen suspected pirates on board were then held and a weapons cache seized. Two Yemeni hostages were also freed.
"These ships provide the pirates with a floating base. They pose a great threat to the merchant shipping," the chief officer of the Danish warship said.
"We have now eliminated one of these threats," Commander Haumann of HDMS Esbern Snare warship said.
The Nato mission said the incident happened on Saturday morning, when the warship came across a suspicious vessel with two skiffs on deck.
It said it believed the fishing vessel had been hijacked.
The Nato mission - alongside with the EU's naval force - has been escorting merchant ships in the Gulf of Aden since 2008.
Earlier this week, the International Association of Independent Tanker Owners (Intertanko) said Somali pirates were now using at least 20 seized vessels as mother ships to launch attacks in the region.
Somali pirates have made millions of dollars in recent years by capturing cargo vessels in the shipping lanes around the Horn of Africa and holding the ships and crew for ransom.
Somalia has had no functioning central government since 1991, allowing piracy to flourish off its coast.
Pirates have greatly expanded the areas where they operate in recent years
Source: BBC News