Vasilevskiy is a product of the Tolpar Ufa system, where after playing in the lower junior ranks he was selected to Russia's 2010 U18 World Junior Championships team. He posted a 2.65 GAA and .897 save percentage in the tournament, but Russia did not medal.
In 2010-2011, Vasilevskiy took over as the co-starter for Ufa's MHL team, posting a 1.81 GAA and .937 save percentage in 14 games. Won bronze with the Russians at the 2011 U18 World Junior Championships after posting a 2.62 GAA and .936 save percentage in 6 games. At the conclusion of the season, he was drafted by parent club Ufa with their 1st round pick, 7th overall, in the KHL Draft.
Became the full-time starter for Ufa's MHL team and shined with a 2.23 GAA and .923 save percentage in 27 games. Named the starter for Russia's U20 World Junior Championship team despite being underage and performed well with a 2.01 GAA and .953 save percentage in 5 games, although he was pulled in Russia's upset win over Canada. Russia went on to win Silver in the tournament. Later selected for a third U18 World Junior Championships. Russia did not medal, but Vasilevskiy had a solid 2.20 GAA and .922 save percentage in 5 games. Finished the season ranked the #1 European goaltender by the NHL Central Scouting Service and was selected in the 1st round, 19th overall, by the Tampa Bay Lightning.