Crimea's Muslim Tatars, generally seen as pro-Kiev, have fled the southern peninsula in their thousands since a separatist referendum that led Russia to annex the province.
Elderly members of the 300,000-strong ethnic group still remember the Kremlin's Soviet-era deportation of Tatars to Siberia.
"Displacement in Ukraine started before the March referendum in Crimea and has been rising gradually since," Adrian Edwards, spokesman for the UN high commissioner for refugees, said as he released the figure.
The true figure may exceed 10,000, Edwards said, because that number only includes people who have registered with local authorities.
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Most have stayed in Ukraine rather than seeking refugee status abroad, he said.
Last week, a UN human rights probe condemned what it said was the harassment and persecution of the Crimean Tatars, in language that sparked an angry rebuke from Moscow.
"Among accounts we're hearing from displaced people is that they have left either because of direct threats or out of fear of insecurity or persecution," said Edwards.
"People cite fear of persecution because of ethnicity or religious beliefs, or in the cases of journalists, human rights activists and among intellectuals due to their activities or professions. Others say they could no longer keep their businesses open," he added.
Edwards said the UN could not say for sure who was responsible for handing out such treatment, nor whether it was part of an organised campaign.