The Liverpool forward took the award in recognition of his hat-trick in the 6-3 victory away at LASK on Wednesday night.
A pair of clinical first-half finishes at Raiffeisen Arena was followed by a close-range tap-in after the break as Barcola opened his account for the Reds in style.
In the voting for Player of the Week in the competition, he was No.1 ahead of Nicolo Tresoldi, Harry Kane and Lamine Yamal.
LASK 3-6 Liverpool: Highlights