Two Turkish helicopters helped repel Sunday's attack on the M/V Diamond Falcon off Yemen's southern coast after the Vietnamese boat issued a distress signal, an army statement said.
The Danish navy told AFP that the pirates, who attacked on two speedboats, fled, and that no arrests were made.
It added that the attack took place in a busy fishing zone, making it easier for the pirate craft to disguise their intent.
The statement did not give their nationality, but more than 100 attacks last year in one of the world's busiest shipping lanes have mostly been blamed on Somali pirates.
The United States, European Union countries, China and Russia have already deployed naval vessels to the region.