A helicopter took off from Dutch frigate De Ruyter early Tuesday after a Panamian-registered vessel said it had felt threatened.
The helicopter intercepted one high-speed boat and detained "some" of the suspects, the ministry said.
Spanish frigate Mendez Nunez dispatched a helicopter which intercepted another speedboat, detaining more suspects, all of whom are now aboard the Dutch ship.
The ministry said those on board the detained skiffs had thrown objects overboard and tried to head off in different directions.
After a spike at the start of the last decade, successful pirate attacks on commercial vessels sailing off the Horn of Africa have diminished, deterred by the European Union Naval Force's anti-piracy operation Atalanta.