Competing internationally with the Russian national junior team, Barbashev won gold at the 2012 World U-17 Hockey Challenge, played at the 2012 Ivan Hlinka Memorial Tournament, placed fourth at the 2013 IIHF World U18 Championships, and won bronze at the 2014 World Junior Ice Hockey Championships. At the 2014 World Juniors, he was the youngest player on the Russian team, and had one goal and one assist.