Warships typically do not intervene in hijackings because of the danger that crews may be hit by crossfire.
Forces were able to intervene in this case because the ship had registered with naval authorities, was travelling along a recommended transit corridor and was part of a group transit, ensuring the ships had a helicopter within 30 minutes' reaction time, Harbour said.
"There's been many instances where there's been excellent co-operation and three, four or even five nations have helped deter a pirate attack, he said.
"But this is the first where a warship has been able to send forces to stop a hijacking while it was in progress."
Denmark rarely releases information on operations carried out by its elite forces, but the storming of the ship may have been carried out by the country's elite Frogman Corps, which were part of a Nato deployment.
"There is an operation going on down there and we're involved. It is still going on right now," Pernielle Kroer, spokeswoman for the Danish navy told the Associated Press news agency.
Other forces have intervened in pirate hostage situations, but not during the hijacking itself.
Details on the nationalities of the crew on board the Arielle and its cargo were not immediately released.
Somali pirates have seized three ships this year and are holding hostage more than 180 crew members and a total of nine vessels.