He moved to Seoul at age 16 and attended high school there with Lee Duck-hee, another future ATP Tour player.

[1] Kwon made his tour-level and Grand Slam debut after winning the 2018 Asia-Pacific Wildcard Playoff for the main draw of the 2018 Australian Open.

In February 2020, Kwon reached four consecutive ATP Tour-level quarterfinals in Pune, New York, Delray Beach and Acapulco.

Kwon reached the third round of a Grand Slam for the first time in his career at the 2021 French Open where he defeated South African Kevin Anderson and Andreas Seppi before losing to another Italian ninth seed and eventual quarterfinalist Matteo Berrettini.

Despite losing in qualifying at the Eastbourne International, Kwon entered with a second-round bye as a lucky loser after Reilly Opelka withdrew.

Kwon was competing in his maiden ATP Tour semifinal after winning his first quarterfinal in his eighth attempt against Ilya Ivashka.

120 at the Japan Open, he reached the quarterfinals for a second time at the ATP 500-level defeating sixth seed Alex de Minaur and Mackenzie McDonald.

In December 2024, Kwon announced that he would step away from tennis and fulfill his mandatory military obligation, which began in January 2025.

[12] He was first nominated to the team for the 2017 Davis Cup, making his debut against Uzbek tennis player Denis Istomin.

Kwon represented South Korea at the 2022 Davis Cup Finals and recorded his first victory over a top-20 player by defeating world No.