Adrian Edwards, spokesman for the UN high commissioner for refugees, said that over 11,000 people had crossed into Ethiopia in the past 72 hours.
The wave began after South Sudanese government forces captured the rebel stronghold of Nasir at the weekend.
The refugees, all from the ethnic Nuer population of South Sudan, crossed the Baro River which marks the border with Ethiopia.
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"The refugees tell us that more people are on their way, with many amassed on the South Sudanese side of the border waiting to cross the river on one of the few small ferry boats," Edwards said.
Aid agencies were rushing food and medical supplies to the newly-arrived refugees, some of whom were wounded, said Edwards.
Efforts were under way to move them to a camp deeper inside Ethiopia, but with that site fast approaching its capacity of 40,000, a new location was being set up to take in another 30,000.
"The vast majority of new arrivals are still women and children, but we are also seeing an increasing number of men fleeing," said Edwards.
More than 110,000 refugees have fled South Sudan to Ethiopia since the outbreak of violence there last December.
Another 205,000 have headed to Uganda, Sudan and Kenya, while some 923,000 are displaced inside South Sudan itself.
South Sudanese President Salva Kiir has been locked in battle for four months with rebels loyal to sacked vice president Riek Machar.
The conflict has pitted members of Kiir's Dinka tribe against Machar's Nuer.
Both sides have been implicated in atrocities and war crimes.
The war has left thousands and possibly tens of thousands of people dead, and sparked a massive humanitarian crisis.
