The 25-year-old man, who was sought by the Austrian authorities, was detained at the Polish border post of Dorohusk as he was trying to cross over into Ukraine, the border police said in a statement.
He is "suspected of having taken part in the armed conflict in eastern Ukraine and killing prisoners and wounded fighters," it said.
Austrian prosecutors said there was a European arrest warrant for the man for suspected war crimes, adding that they believed he was fighting on the "Ukrainian side."
However, Dariusz Sienicki, a spokesman for the Polish border police, had told AFP earlier that the man was "a member of a separatist group."
Extradition proceedings have been launched to return him to Austria.
More than 10,000 people have been killed since the start of a pro-Russian insurgency in April 2014 which Kiev and the West accuse Moscow of masterminding.
Although the violence has ebbed in the wake of several cease-fire accords, efforts to secure a peace deal have ground to a halt amid sporadic clashes, and neither side appears prepared to make concessions.