At least 26 passengers were rescued from the water after a major search operation in the early hours, President Abedrabbo Mansour Hadi said in a statement on the official sabanew.Net website.
The ship sank northwest of Socotra - around 350 kilometres from Yemen's south coast - which has been hit by rare tropical cyclones in recent months.
Hadi called for "doubling efforts to broaden rescue operations to reduce the scope of the catastrophe that has struck the inhabitants of Socotra."
"Sixty people, including women and children, were aboard the vessel, which was also carrying small fishing boats," he said.
The government said United Arab Emirates jets were assisting search and rescue operations alongside Yemeni coastguards as well as two ships from Australia and Austria.
It did not specify whether those vessels were merchant ships or part of an international flotilla that has been fighting piracy off the nearby Somali coast.
Although long ruled from Yemen, Socotra lies closer to the coast of Africa than it does to the Arabian Peninsula.
For years it was prey to piracy from the lawless Somali coast and it is in one of the most heavily patrolled maritime areas on Earth.
Kavieen did not specify whether warships of the international counter-piracy operation were taking part in the search for survivors.
He said that the ship had been out of contact for several days and its sinking was confirmed today.
"Vessels have been combing the area since the early hours and there is significant hope that the passengers have survived," he said.
The port of Mukalla, from which the sunken freighter set off, was controlled by Al-Qaeda for a full year until it was retaken by pro-government forces in April.
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