A total of 58 passengers were on board the vessel which set sail on Saturday before capsizing in rough seas on Wednesday.
Survivors told how the three smugglers crewmen forced 22 people overboard when the boat’s engine failed soon after departure, the Office of the UN High Commissioner for Refugees said.
“UNHCR is deeply saddened by the tragic loss of life,” the agency said in a statement.
An investigation is under way, it added. “We hope that the perpetrators will be brought to justice.”
The bodies of the 11 dead were recovered on beaches around Ceelaayo village, about 30 kilometres west of the Somali port town of Bossaso.
Locals found 13 survivors, including two women and a teenage boy and girl, most of whom were treated for skin burns caused by fuel inside the boat.
Last year a record 103,000 refugees, asylum seekers and migrants crossed the Gulf of Aden and Red Sea from the Horn of Africa — mainly Somalis and Ethiopians. A reported 130 drowned.