Spokesman Kris Janowski said the increase followed intensified fighting between government forces and UNITA rebels in Angola's Cuando-Cubango province.
The refugees, mainly women and children, are arriving on foot from the Lulana and Jamba areas of Angola, he said, and are suffering from malaria, diarrhoea, skin disease and in some cases gunshot wounds.
UNHCR is opening a transit camp in Sijembela near the border, where more than 7,500 refugees have arrived since 1 January, the spokesman added. The UN agency is hoping to transfer these people to another camp, Mayukwayukwa, which is already home to more than 6,000 refugees, but this may be delayed by several months by rains.
Since fighting in Angola intensified last October a total of 20,500 refugees have crossed into neighbouring Zambia, which already hosts more than 200,000 refugees from Angola, the Democratic Republic of Congo, Burundi, Rwanda and Somalia, according to UNHCR.