Shipping firms have since December diverted hundreds of vessels around southern Africa's Cape of Good Hope in order to avoid attacks by the Iranian-backed Houthis. The journey around Africa takes 10-14 days longer and is more costly than the passage via the Red Sea and Suez Canal.
"Someone has to stand up for free world trade, and we have taken on the responsibility to help make that happen," Defence Minister Troels Lund Poulsen told reporters on board the frigate Ivar Huitfeldt before it departed the Korsor naval base.
The attacks target a route that accounts for about 15% of the world's shipping traffic and acts as a vital conduit between Europe and Asia.
Denmark, home to shipping company Maersk, is sending the frigate to the area as part of Operation Prosperity Guardian formed last month aimed at protecting merchant vessels.
The Danish Parliament is expected to approve a resolution to send the warship into the area on Feb. 6, the Defence Ministry said.
(Reporting by Jacob Gronholt-Pedersen and Louise Rasmussen, Editing by Angus MacSwan)
