Ukrainian military spokesman Andriy Lysenko said the incident occurred close to the government-held village of Granitne, about 50 kilometres south of the rebels' de facto capital Donetsk.
With the heaviest fighting easing, most of the Ukrainian casualties reported in the past few months have come from situations of soldiers setting off trip wires or stepping on mines that litter the industrial war zone.
In a rare admission of their own losses, a senior rebel official told AFP that Ukrainian forces had killed nine pro- Russian fighters since Saturday.
More than 9,000 people have died and more than 1.5 million driven from their homes since the predominantly Russian- speaking Donetsk and Lugansk regions revolted against Ukraine's new pro-Western government in April 2014.
A series of truce agreements have helped significantly reduce the violence, although sporadic exchanges of small weapons fire continue along the 500-kilometre front.
Kiev and the West accuse Russia of supporting the insurgents and sending regular troops across the border, claims that Moscow denies.