Using a pick acquired from Sherbrooke, the Wildcats selected the five-foot-11, 175-pound captain of the Russian under-17 team.
Barbashev is eligible for the NHL draft in 2014.
"He was captain of his team and competes hard every shift," Danny Flynn, Moncton's head coach and director of hockey operations, said in a release. "We feel he has the potential to develop into a great two-way offensive forward for our team."
German left-winger Leon Draisaitl went to Prince Albert next. The six-foot-two 198-pounder had 21 goals and 35 assists in 35 games last season for Jungadler Mannheim Under-18.
Third was Swedish goalie Oscar Dansk (Erie), followed by Czech left-winger Martin Reway (Gatineau via P.E.I.) and Finnish goalie Joonas Korpisalo (Prince George).
Each CHL team is allowed two European import players per season.
Last year the London Knights took defenceman Olli Maatta first overall. He was taken 22nd overall by the Pittsburgh Penguins at the recent NHL draft.
Forward Nail Yakupov, who went second in last year's CHL import draft, was the first overall pick of the Edmonton Oilers in the NHL draft.