[2] According to some mass media reports, Andrey allegedly had problems with his back since his childhood, so he attended manual therapies.

[3][4] Kuznetsov played his first ITF junior tournament at the 2006 Black Gold of Udmurtia, but received a walkover in the qualifying round.

[6] He made his first main draw Grand Slam appearance at the 2010 Wimbledon Championships where he lost in five sets to the 31st seed Romanian Victor Hănescu.

[7][8] At Wimbledon in 2014, Kuznetsov recorded his first win over a player ranked inside the world's top-10 by defeating seventh seed David Ferrer in five sets.

[15] After a first round loss to fifth seed Jo-Wilfried Tsonga in Doha,[16] Kuznetsov made his maiden ATP semifinal appearance in Sydney where he fell to fellow first time semifinalist Dan Evans in another three setter.

[18] In the first round of the Davis Cup World Group, he teamed up with Konstantin Kravchuk in Russia's doubles rubber against Serbia but they lost in four sets to Viktor Troicki and Nenad Zimonjić.

[19] A week later, he lost to Troicki and Zimonjić again, this time in the doubles final of the Garanti Koza Sofia Open.

[21] Kuznetsov began his clay season in Monte Carlo where he qualified for the main draw following wins over established players Julien Benneteau and Mikhail Youzhny.

[22] He reached his second quarterfinal of the year at the inaugural Hungarian Open[23] where he upset the third seed Fabio Fognini en route.

He then beat 7th seed Diego Schwartzman in the quarterfinals in straight sets to eventually lose to Alexandr Dolgopolov in the semifinals.

[25] Kuznetsov's only tournament of 2018 was when he participated in the Koblenz Challenger, taking place in January and lost his first round match against alternate player Ilya Ivashka.

[28] Kuznetsov won his first challenger title in close to six years at the 2021 President's Cup II defeating Jason Kubler in the final.

[31] At the 2023 Winston-Salem Open he entered the singles main draw as a lucky loser directly into the second round after the withdrawal of 16th Emil Ruusuvuori.