2009-10: Andrey Vasilevskiy played for Salavat Yulaev's 1994-born team and represented Russia at the 2010 U18 World Junior Championship. Salavat finished second in the Ural Region. Vasilevskiy appeared in five games for fourth-place Russia at the U18 WJC and was 2-2 with 1 shutout. He had a 2.65 goals against and .897 save percentage in the tournament.
2010-11: Vasilevskiy skated for Tolpar Ufa in Russia's MHL (junior league) and played for Russia at the 2011 World Junior Championship. Vasilevskiy appeared in 14 games as a backup to 22-year old Rafael Khakimov for Tolpar Ufa as Tolpar finished with the league's best record. He finished the season with a 1.81 goals against and .937 save percentage. He played in two playoff games and had a 2.05 goals against and .936 save percentage. Tolpar defeated Khimik in the third place series after falling to Magnitogorsk in the East Conference Finals. Vasilevski played in 6 of 7 games for Russia at the U18 WJC, including the bronze medal game win over Canada, and was 4-2 with a 2.62 goals against and .936 save percentage. Vasilevskiy was selected by Salavat Yulaev in the first round (seventh overall) of the 2011 KHL Draft.
2011-12: Vasilevskiy skated in 27 games with Tolpar, again sharing the goaltending duties with Khakimov, and represented Russia in four tournaments at three age levels. Vasilevskiy had three shutouts and posted a 2.23 goals against and .931 save percentage as Tolpar finished second in its division in the regular season. He started two of three playoff games and was 0-2 with a 2.50 goals against and .943 save percentage. Vasilevskiy opened the season skating for Russia at the 2011 U18 Ivan Hlinka Tournament and in four games was 1-2 with a 3.14 goals against and .906 save percentage. At the 2012 U20 World Junior Championship he was 4-1 with 2 shutouts and had a 2.01 goals against and .953 save percentage in five games. Andrey Makarov was in net for Russia in the gold medal game, a 1-0 overtime loss to Sweden. Vasilevskiy was 1-2 with a 3.29 goals against and .926 save percentage in the 2011 U19 World Junior A Challenge. He played five games as Russia finished fifth in the 2012 U18 World Junior Championship and was 2-3 with 1 shutout with a 2.20 goals against and .922 save percentage. Vasilevskiy was invited to the NHL Draft Combine and was the top ranked European goalie in Central Scouting's final rankings prior to the 2012 NHL Draft.
2012-13: Vasilevskiy made his KHL debut, appearing in eight games for Ufa Salavat Yulaev – and played for Ufa's U22 team Tolpar in the MHL. He also played for Russia's U20 team in the World Junior Championship – which was held in Ufa. Vasilevskiy was 4-1 with a 2.22 goals against and 2.32 safe percentage in KHL play. He had the MHL's top save percentage (.930) and goals against (1.93) and was 17-6 in 27 regular season games for Tolpar. In three playoff games he was 0-2 with a 2.85 goals against and .897 save percentage. Vasilevskiy split the goaltending for Russia's U20 team with Andrei Makarov, appearing in four games where he went 2-1 with 1 shutout, posting a 1.81 goals-against and .950 save percentage. Russia defeated Canada in overtime in the tournament's bronze medal game.
Vasilevskiy returned to Russia to play for Ufa Salavat Yulaev in 2013-14.