The crew members were believed to be unharmed in the attack, which occurred at dawn.
The incidents happened a day after the Portuguese navy successfully thwarted an attempted pirate attack on a Norwegian oil tanker in the Gulf of Aden, about 161km from the Somali coast.
The Portuguese warship, the Corte Real, sent a helicopter to the area to help the Kition after a distress call was made.
"It is the first time we have spotted high explosives on board a pirate ship, normally [Somali pirates] just stick to AK-47s and RPGs (grenades)"
Alexandre Santos Fernandes, Nato spokesman
The Corte Real, part of a Nato naval escort patrol, destroyed explosives they discovered on board their boat when they arrested at least 19 armed pirates.
The Portuguese helicopter chased the pirates back to their "mother ship", or command vessel, and briefly detained about 19 pirates, Alexandre Santos Fernandes, a Nato spokesman, said.
Explosives and grenade launchers were discovered on the mother ship when Portuguese special forces boarded "with no exchange of fire", he said.
"It was almost a kilogramme of high explosives. If used correctly it can open a hole in the hull of a ship and sink her."
"It is the first time we have spotted high explosives on board a pirate ship, normally they just stick to AK-47s and RPGs (grenades)."
The pirates were disarmed and then released, as Nato patrols have no authority to make arrests.