It was not clear what caused the boat to capsize.
It is the second accident involving migrants off Yemen in about a week.
On February 20, six African migrants drowned and 11 were reported missing, presumed dead after traffickers pushed dozens of passengers overboard in deep waters off Yemen's south-eastern coast.
Smugglers forced the 52 passengers - 40 Somalis and 12 Ethiopians - into the sea after they spotted Yemeni coast guards onshore.
At least 35 people reached the shores, the UN High Commissioner for Refugees
Many African migrants, mostly from conflict-torn Somalia, try to reach Yemen, which is seen as a gateway to Europe and the oil-rich countries of the Arabian peninsula.
Hundreds of people perish every year in the perilous exodus that takes thousands of desperate Somalis and Ethiopians to Yemen in small boats run by human traffickers operating from Somali ports.
Since the beginning of the year, 168 boats carrying 9,449 people have reached the Yemeni coast.
At least 47 people died while trying to reach Yemen by sea from Somalia during the same period, according to the UNHCR.
At least 590 people drowned and another 359 were reported missing last year as result of crossings gone wrong, often with traffickers forcing the migrants overboard, UNHCR said.