The military said the death occurred yesterday in the village of Kurti Blaka, some 15 kilometres north of the militias' de facto capital of Donetsk.
The rebels did not report any casualties on their part and the Ukrainian military did not specify how the soldier died.
The death comes amid fresh hope that the 31-month conflict may be winding down after nearly 10,000 people have been killed.
The former Soviet republic accuses its neighbour Russia of launching the war in retaliation for Kiev's ousting of a Moscow-backed president in February 2014.
The reported death does not necessarily mean the collapse of the ceasefire because monitors from the Organisation of Security and Co-operation in Europe (OSCE) have reported a significant decrease in fighting in the past two weeks.
But it does mean sporadic violence is likely to continue and that shelling across the front line may go on even as the sides talk peace.
The insurgents agreed to the truce last Friday -- two days after it was negotiated by Ukraine and Russia with the help of mediators from the OSCE.
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