As a junior, she won the girls' doubles event at the 2015 US Open alongside Aleksandra Pospelova, defeating Kalinskaya and Anastasia Potapova in the final.

She continued her success at majors as a senior, reaching the 2019 US Open semifinal in the women's doubles alongside Aliaksandra Sasnovich, where they lost to Ashleigh Barty and Victoria Azarenka.

[5] She began playing on the ITF Junior Circuit in January 2012 at age 13, and in September of the same year won her first singles and doubles titles at the low-level Grade-5 Mostar Open.

[6][7] During her quarterfinal match at the 2013 Losinj Juniors Cup, against another Slovakian player, Nikola Dolakova, she was forced to retire in the second set due to injury.

A month later, partnering with Kristína Schmiedlová, she won the doubles title at the Grade-1 Mediterranee Avenir in Casablanca, after being awarded a walkover victory due to the withdrawal of Ioana Ducu and Anna Bondár.

Kužmová made her junior Grand Slam debut in 2014 at the French Open, reaching only the first round in both the singles and the doubles.

[13] She also qualified for the Linz Open and marked her first singles win on WTA Tour, defeating Anna-Lena Friedsam before she lost to another German player, Tatjana Maria.

[16] Her first event in 2018 was the Auckland Open, where she reached the main draw and marked her first win in 2018, defeating Jade Lewis but lost to Julia Görges in the second round.

[17] At her first Australian Open, she qualified but still was not ready to mark her first Grand Slam main-draw win, losing to Elise Mertens.

[21] She started grass-court season, reaching her second WTA singles semifinal at the Rosmalen Championships, where she lost to Kirsten Flipkens.

She finished her grass-court season with her main-draw debut at Wimbledon, where she was defeated by Rebecca Peterson – but with that match she completed participation at all four Grand Slam events in the main draw.

[16] Kužmová started the year really well, getting to the semifinal at the Auckland Open, where Julia Görges stopped her achieving her first WTA singles final.

[31][32] At the Dubai Tennis Championships, she reached her first Premier 5 quarterfinal, winning against Pera, Kiki Bertens and Sofia Kenin, before she lost to Petra Kvitová.

[36] She then lost in the first round of the Istanbul Cup to Barbora Strýcová, followed by another first-round loss at the Prague Open to Anna Karolína Schmiedlová.

[42] After the clay-court season, Kužmová did not do well, losing in the first round at all of the grass tournaments: at the Rosmalen Championships to Margarita Gasparyan, at the Mallorca Open to Maria Sharapova, and at Wimbledon to Polona Hercog.

The most significant one is Premier-level St. Petersburg Trophy, where she partnered with Anna Kalinskaya and lost to Russian combination Gasparyan and Ekaterina Makarova.

[55] At the newly introduced International-level Lyon Open, she got to her first singles quarterfinal in 2020, before losing to Anna-Lena Friedsam and also reaching the semifinal in doubles.

[61] Partnering Natela Dzalamidze, Hrunčáková won the doubles title at the Linz Open, defeating Anna-Lena Friedsam and Nadiia Kichenok in the final.

[62] She entered the French Open as a lucky loser after an absence in the main draw at this major since 2020, but lost in the first round to 28th seed Elise Mertens.

[72] Again entering as a lucky loser at the Guangzhou Open, she defeated Anna Kalinskaya[73] and wildcard Yue Yuan[74] to reach the quarterfinals where she lost to Wang Xiyu in three sets.

[77] At the 2024 Billie Jean King Cup finals, Hrunčáková helped Team Slovakia reach the quarterfinals in doubles by pairing with Tereza Mihalíková to beat the United States 2-1 in the tie after defeating Ashlyn Krueger and Taylor Townsend.

In the semifinals against Great Britain, Hrunčáková was defeated by Emma Raducanu, but later redeemed herself by winning the deciding doubles match with Mihalíková against Olivia Nicholls and Heather Watson.

During the round-robin, Kužmová won all of her three singles matches against Tessah Andrianjafitrimo from France, Habiba Lasheen from Egypt and Chihiro Muramatsu from Japan.

Kužmová won her singles match against Maia Lumsden, but lost in the doubles alongside Martina Okalova to Emily Arbuthnott and Ema Lazic.

In a decisive match against Lidziya Marozava and Vera Lapko, Kužmová and Anna Karolína Schmiedlová failed to send their country in the World Group.

[83][84] The following year, in her first match in the World Group II play-offs against Brazil, she faced Beatriz Haddad Maia and won.

[85] Since it was obvious that Slovakia had won, Kužmová's match against Carolina Alves was cancelled but she played doubles alongside Rebecca Šramková and they lost in straight sets.

[87] In November 2024, Hrunčáková partnered Tereza Mihalíková to win the deciding doubles match against the USA pair of Taylor Townsend and Ashlyn Krueger that saw Slovakia qualify for the 2024 Billie Jean King Cup quarterfinals.

[90][91] Hrunčáková lost to Emma Raducanu in the opening singles match of the semi-final against Great Britain, but returned to partner Mihalíková to defeat Olivia Nicholls and Heather Watson in the doubles and earn Slovakia a place in the final for the first time since 2002.

[104] Kužmová was nominated for the 2018 Fed Cup Heart Award, after making two important wins against Aryna Sabalenka and Aliaksandra Sasnovich, but lost to Eugenie Bouchard.