UNHCR, the United Nations refugee agency said the boat foundered on Saturday in the Gulf of Aden between Bir Ali and Mayfa'a Hajar. It had sailed from the village of Shimbirale in northeastern Somalia, near Bosaso, a major departure port for smugglers.
The boat was carrying about 110 Ethiopians, 10 Somalis and five crew, the UNHCR said in a statement released from Geneva on Sunday.
Authorities had recovered 22 bodies, but survivors reported another 28 people were missing.
Yemeni authorities had detained 43 Ethiopians -who unlike Somalis do not get automatic refugee status in the country - but another 22 had fled, the UNHCR said. Two of the boat's crew members were arrested by police, while three escaped.
The UNHCR said on Friday that twenty mainly Somali migrants had died of hunger and thirst while travelling on a boat bound for Yemen, where they sought a better life.
Thousands of Somalis undertake the perilous voyage to Yemen each year, including about 100 per day during the period of good sailing weather between September and March.
There are more than 80,000 registered refugees in Yemen, nearly all Somalis, but it is estimated that there are hundreds of thousands more, according to the Geneva-based agency.