The clash, reported by the military on Facebook, occurred near the town of Schastye in the rebel region of Lugansk.
The insurgents also opened fire on several checkpoints located near the towns of Krimskoye, Donetski and Olchovoye.
Another soldier was reported wounded in bombing on the outskirts of Donetsk airport, according to Ukrainian officials.
A truce was declared Sep 5 in the conflict zone, but both sides have accused each other of breaking it.
According to media, since the ceasefire was agreed in the Belarusian capital of Minsk, more than 400 people have been killed, including civilians, militias and military personnel.