Dozens of Yemenis have crossed the Gulf of Aden in small boats to get to Somalia, Djibouti and Somaliland to escape fighting and Saudi air strikes, the UN refugee agency has said.
The UNHCR said it was looking for a possible site for the refugees in Djibouti in case the fighting worsens.
At the same time Somali refugees are still continuing to arrive in Yemen to escape violence and poverty at home.
Yemen hosts more than 238,000 Somali refugees, the UNHCR says.
The UNHCR said that at least 32 Yemenis "fleeing conflict" landed on Somalia's northern coastline after crossing the treacherous Gulf of Aden and landing in the semi-autonomous regions of Somaliland and Puntland.
BBC Africa analyst Mary Harper says that the idea of Yemenis seeking refuge on Somali soil is striking - because it is normally a place to run away from, not towards.
The UN says the authorities in the Somaliland port town of Berbera - on the Gulf of Aden - are doing what they can to help.
About 12 Yemeni families recently arrived at Berbera after travelling from Yemeni's third largest city of Taiz, where Saudi planes targeted Houthi rebels, officials said on Tuesday.
In the meantime, hundreds of migrants are continuing to flood in the opposite direction, from Somalia to Yemen. The UN said more than 1,500 arrived last week alone.
Concerns are also being raised in Somalia over potential recriminations against Somali refugees in Yemen after the Somali government voiced its support for the Saudi-led air strikes against Houthi fighters.