Alexander Bublik began his career on the ITF Future Tour , on which he has won four singles titles and three doubles titles. He made his debut on the ATP World Tour in September 2016 in St. Petersburg , when he started in the main field thanks to a wildcard in both singles and doubles. He lost both games. At the Australian Open 2017 , he qualified for the first time for the main draw in a Grand Slam tournament and also won his opening game against Lucas Pouille, who was in 16th place, in four sets. He was eliminated in round two against Malek Jaziri without winning a set. He won his first title on the ATP Challenger Tour in February 2017 when he beat Chilean Nicolás Jarry in straight sets at the Morelos Open .
In November 2016, Bublik announced that it would play for Kazakhstan instead of his native Russia. In 2019 he made his debut for the Kazakh Davis Cup team .