Kužmová started playing tennis at the age of four under her father's care. She prefers clay courts and plays mainly in tournaments of the ITF Women's Circuit , in which she has already won 14 singles and six doubles titles.
Kužmová was able to record considerable success at a young age. In 2014 she won the U14 team world championship for girls in Prostějov , Czech Republic, together with her Slovak teammates Tereza Mihalíková and Tamara Kupková, and won her first professional title on the ITF tour in an individual, and in 2015 she triumphed alongside Alexandra Pospelowa in the women's junior competition of the US Open after winning the final against Anna Kalinskaja and Anastassja Potapowa . A year later she reached the final in New York , in which she was defeated by Kayla Day .
Immediately thereafter, Kužmová won her first victory in an ITF tournament in the $ 25,000 category in Lubbock and was in two more ITF finals in Australia by the end of the season. After winning another title in Mildura , she took part in the qualification of a Grand Slam tournament for the first time at the French Open 2017 and lost there in the second round. At the US Open she managed to jump into the main field; At the beginning she had to admit defeat to Venus Williams in three sets. In Linz , also coming out of the qualification, she was able to record her first victory in the main draw of a WTA tournament against Anna-Lena Friedsam .
After moving into the semi-finals in Budapest 2018 as a lucky loser, in which she was defeated by the eventual winner Alison Van Uytvanck and another tournament victory on the ITF tour in Shenzhen , Kužmová was included in the top 100 of the world rankings for the first time . Her biggest individual title to date, she won in front of her home crowd at a tournament in the $ 100,000 category in Trnava , which she won in the final against Verónica Cepede Royg . Then she was in Paris after a success over the former tournament winner Francesca Schiavone for the first time in the second round of a Grand Slam tournament. Further successes on the ITF tour, such as triumphing in the final of Budapest over Jekaterina Alexandrowa and reaching the final in Dubai , where she lost to Peng Shuai , put her in the top 50 of the world rankings.
It was also in Dubai where Kužmová caused a sensation for the first time at a WTA tournament in the premier category at the Dubai Duty Free Tennis Championships 2019 , when she beat a player from the top 10 in the world with Kiki Bertens and made it to the quarter-finals in which she had no chance against Petra Kvitová . 2019 was also a very successful year for Kužmová in doubles. So she won her first two WTA titles, in Prague together with Anna Kalinskaja after winning the final over Nicole Melichar and Květa Peschke, and in Bucharest alongside Kristýna Plíšková after a two-set win against the Romanian duo Jaqueline Cristian and Elena-Gabriela Ruse . At the US Open , together with Aljaksandra Sasnowitsch, she even made it into her first Grand Slam semi-final; there they managed against Ashleigh Barty and Wiktoryja Asaranka but only one game win. Kužmová was able to reach the third round in singles in Miami , Madrid and at the French Open , also there after beating Bertens. As a result, she rose in the world rankings to position 43; after the recently weaker results at the end of 2019 and the beginning of 2020, it fell slightly again.
In 2018 she played for the Slovak Fed Cup team for the first time in a duel against Russia . Since then, she has played a total of eight matches in singles and doubles for her country, of which she was able to win five (individual balance 5: 1).