According to reports confirmed by the UN High Commissioner for Refugees (UNHCR), the boat had 32 Yemenis.
Yemen is currently embroiled in heavy fighting with Saudi Arabia conducting airstrikes against Shiite militias from the Houthi community.
Reports also indicated that the Yemeni refugees were from Taiz city and that they took 12 hours to cross the Gulf of Aden.
Taizz city which lies between the Yemeni capital Sanaa and the port city of Aden was last week taken over by the Houthi rebels who have driven the beleaguered Yemeni President Abd Rabbuh Mansur Hadi into exile.
Berbera town is governed by the self-declared Republic of Somaliland; it has not issued a statement concerning the arrival of the refugees.
Meanwhile, Somali Minister for Foreign Affairs Abdisalam Hadliye Omar said on Monday that his government had requested UNHCR to assist in evacuating Somalis caught up in the fighting in Yemen.
Hundreds of thousands of Somalis fleeing civil war in Somalia crossed to Yemen over the past two decades.
However, the 32 Yemenis who reached Berbera mark the first lot of refugees to cross from the other side.