2010-11: Andrey Kuzmenko played for CSKA Red Army's 1996-born team and participated in the 2011 Tretiak Cup. In 28 regular season games he scored 19 goals with 23 assists and had 20 penalty minutes. He scored 2 goals and was -1 with 2 penalty minutes in five games at the Russian championships. Kuzmenko scored 4 goals with 2 assists and 6 penalty minutes in eight games at the Tretiak Cup.
2011-12: Kuzmenko was on of the CSKA Red Army 1996-born team's top scorers as the club again reached the Russian championships. He scored 21 goals with 17 assists during Moscow group play and in six games at the Russian championship he scored 2 goals with 4 assists and was +2 with 2 penalty minutes.
2012-13: Kuzmenko made his debut in Russia's U22 MHL as a 16-year-old and dominated against players his own age with the CSKA 1996-born team. He played for Russia's U17 team in the European Youth Olympic Festival and at the 2013 World Hockey Challenge in Canada. In 49 MHL games for CSKA Red Army he scored 5 goals with 7 assists and was an even plus/minus with 8 penalty minutes. Red Army finished 14th in the West Conference. Kuzmenko had 1 assist and 4 penalty minutes in three games at the EYOF. He scored 1 goal with 2 penalty minutes at the WHC. Russia reached the gold medal game against Sweden.
2013-14: Kuzmenko skated for CSKA Red Army's champion MHL team and played for Russia in the 2013 World Junior A Challenge. He scored 13 goals with 18 assists and was +17 with 2 penalty minutes in 36 regular season games. CSKA finished second in the Central Division and defeated JHC Spartak in seven games in the playoff finals. Kuzmenko scored 3 goals with 3 assists and was +4 in 18 playoff games. In five games at the WJAC he scored 2 goals with 1 assist as Russia captured a silver medal. Kuzmenko was ranked 26th amongst European skaters in Central Scouting's final rankings prior to the 2014 NHL Draft.