More than 2,000 Ethiopians have crossed into Kenya seeking refuge, Red Cross has announced.
They fled after several civilians were killed in what the Ethiopian military said was a botched security operation targeting militants.
Addis Ababa announced on Sunday that soldiers had been deployed to the Moyale area in Oromiya, a region that shares a border with Kenya, in pursuit of Oromo Liberation Front fighters who had crossed into the country from Kenya.
But faulty intelligence led soldiers to launch an attack that killed nine civilians and injured 12 others, the state-run Ethiopian News Agency said.
"The Kenya Red Cross Society has received at least 2,000 Ethiopian asylum seekers in Moyale Town following their displacement from Ethiopia," the aid organisation said in a statement late Monday.
The Oromo Liberation Front is a secessionist group which the government has branded as terrorist.
The Oromiya province has been plagued by outbreaks of violence even though Ethiopia declared a six-month, nationwide state of emergency last month.
The Kenyan Red Cross said refugees from Ethiopia had begun to arrive in Kenya on March 10, the majority being women and children.
A state official in the Oromiya region told Reuters on condition of anonymity that tens of thousands of people have also been internally displaced.
The mayor of the Ethiopian town of Moyale was not immediately available to give details.
Ethiopia has said that five soldiers who took part in the attack have been "disarmed" and are under investigation, while a high-level military delegation has been dispatched to the area to launch an inquiry.
Addis Ababa imposed a state of emergency a day after Prime Minister Hailemariam Desalegn announced his resignation in what he said was a bid to smooth the way for reforms.
His successor as premier and chairperson of the ruling EPRDF coalition is expected to be named before the end of this month.