The fire broke out at around 9.30 am on a small cargo vessel anchored near shore off Lien Huong Commune.
Border guards and local authorities were searching for the missing crew member, according to the Lien Huong Port Border Guard Station.
Nearby fishermen rushed to the scene to help extinguish the fire and rescue those on board.
Two crew members were pulled from the water and brought safely ashore, while the third remains missing.
Authorities said firefighting efforts were hampered by the offshore location of the blaze and difficult access to the vessel.