Fighting escalated in March when Saudi-led airstrikes began targeting Yemen's Huthi rebels to defend embattled President Abedrabbo Mansour Hadi.
"Close to 70,000 people fleeing the crisis have arrived in Djibouti, Ethiopia, Somalia and Sudan," the UN refugee agency (UNHCR) and International Organization for Migration (IOM) said in a statement.
"Up to 44,080 people are reported to have arrived in Saudi Arabia and Oman."
The IOM said the number of people fleeing Yemen to neighbouring nations could rise to over 200,000 by the end of next year.
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"Refugees and migrants arrive after many hours at sea often traumatised and exhausted, with few personal belongings, and in urgent need of food, water and emergency healthcare," top IOM official Ashraf El Nour said, at a meeting in the Kenyan capital to coordinate the response to the crisis.
"The most pressing response therefore is to address their basic needs, and to register and provide documentation to enable access to essential services."
The UN says the Yemeni conflict has killed about 5,000 people and wounded 25,000, among them many civilians.
Tens of thousands of Somali refugees have also fled back home from Yemen, adding to three million already in need in the Horn of Africa nation.
Most of the Somali refugees, who originally fled hunger and conflict in Somalia before being caught up in war in Yemen, have crossed the Gulf of Aden by boat to the Horn of Africa country's northern Somaliland and Puntland regions.