The UN is carrying out a humanitarian mission in the war-torn republics of Lugansk and Donetsk.
The world body's office in Kiev said it had mobilised all channels to ensure its unnamed staff member's immediate and unconditional release.
"The United Nations is deeply concerned about the fact that one of its staff members is being held captive in Donetsk," the United Nations said in a statement.
It added that "the staff is well treated" but provided no details about the person's nationality or when and under what circumstances the capture occurred.
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A series of periodic truce deals in 2015 have abated some of the violence, which Kiev and its Western allies accuse Moscow of stirring and backing, a charge that Russia denies.
On Sunday, the European Union criticised the "unprecedented level of violence" in eastern Ukraine after international peace monitors came under fire.
The Organization for Security and Co-operation in Europe (OSCE) said Saturday that several monitors carrying out an observation mission had come under fire 50 kilometres (30 miles) south of the insurgents' de facto capital Donetsk.