Conflict in Chad has led people to cross the border into Sudan's Darfur region, which has been seen as one of the world's worst crises, the UN says.
There are already more than 2m refugees in Darfur
This reversal of previous refugee flows is "a worrisome new development", says the UN refugee agency.
Between 8,000 and 10,000 including "an undetermined number" of Chadians are seeking help after a rebel attack.
The three-year Darfur conflict has led some 2m people to flee their homes and at least 180,000 have died.
In recent months, Chad has been in danger of being drawn into the conflict - with Chad and Sudan swapping accusations of backing the other's rebel groups.
There are some 200,000 Darfur refugees in Chad.
Meanwhile, a senior British official has said he expects targeted sanctions, such as travel bans, to be imposed soon on about 10 Sudanese officials, accused of human rights abuses in Darfur.
The government denies backing the Arab Janjaweed militias accused of mass killings, rape and looting against Darfur's black African population.
A special UN inquiry has given the International Criminal Court in the Hague the names of 51 potential suspects.
The UN is also trying to take control of the Darfur peacekeeping mission from the African Union, which is short of both funds and soldiers.
Sudan, however, is unhappy at this prospect and says the extra money should be given to the 7,000-strong AU mission, rather than set up a new team.