Kovinić started playing as a professional in 2010. Her first WTA Tour singles tournament was the 2013 Budapest Grand Prix, where she became the first Montenegrin to reach the quarterfinals of a WTA event.[2] Her first singles Grand Slam match wins came at the 2015 French Open and the 2015 US Open, and she reached her first singles WTA Tour final at the Tianjin Open, in October 2015.
Her first doubles match on the WTA Tour was at Bogotá, in April 2014. She won her first WTA Tour doubles title with Stephanie Vogt, in July 2015 at Bad Gastein.
2016[]
Kovinić started the season at the Auckland Open. She lost in the first round to third seed Caroline Wozniacki.[3] In doubles, she and Barbora Strýcová reached the final in which they lost to Elise Mertens and An-Sophie Mestach.[4] At the Hobart International, Kovinić was defeated in the first round by Australian wildcard Kimberly Birrell.[5] At the Australian Open, Kovinić made it to the second round and lost to 14th seed and two-time champion, Victoria Azarenka.[6]
Seeded third at the Rio Open, Kovinić advanced to the quarterfinals where she was defeated by wildcard Sorana Cîrstea.[7] Seeded seventh at the Abierto Mexicano, she lost in the second round to Christina McHale.[8] Seeded seventh at the Monterrey Open, she was defeated in the first round by qualifier Nicole Gibbs.[9] At the Indian Wells Open, Kovinić faced eighth seed Petra Kvitová in the second round. She pushed Kvitová to three sets but ended up losing the match.[10] At the Miami Open, Kovinić was defeated in the second round by 24th seed Johanna Konta.[11]
2020[]
At the Australian Open, Kovinić lost in the first round to 16th seed Elise Mertens.[12]
At the Abierto Mexicano, she was defeated in the first round by Kateryna Bondarenko.[13] At the Monterrey Open, she lost in the first round to top seed and eventual champion Elina Svitolina.[14]
In August, Kovinić played at the Cincinnati Open where she was defeated in the first round of qualifying by Vera Zvonareva. At the US Open, she made it to the second round and lost to 24th seed Magda Linette.[15]
2021[]
In January, she started her Australian tour at the Gippsland Trophy with a win against Tamara Zidansek, before losing to Jeļena Ostapenko in the next round. After that, she played at the Australian Open where she lost in the first round against top seed and world No. 1, Ashleigh Barty. Her next tournament was the Phillip Island Trophy where she played against 13th seed Marie Bouzková and retired during the second set after winning the first.
In March, Danka made the round of 16 at the Abierto Zapopan in Guadalajara, Mexico where she was defeated in straight sets by Lauren Davis. During the tournament, she suffered a back injury and had to pull out of Monterrey Open and Miami Open.
In April, Kovinic made it into the quarterfinals of the Charleston Open by beating third seeded Petra Kvitová in straight sets in the round of 16. It was her third victory over a player who was ranked inside top 10. In the next round, she defeated 11th seed Yulia Putintseva to reach her first WTA 500 semifinal. After that, she beat 12th seeded Ons Jabeur in straight sets, to book a place in her third career final which she lost to Veronika Kudermetova.
After that, she entered the MUSC Health Open in Charleston where she reached her second consecutive WTA semifinal by beating Viktoriya Tomova in straight sets, seventh seeded Lauren Davis in the round of 16, and Shelby Rogers in the quarterfinals. She then lost to the top seed Ons Jabeur.
2022[]
In January, she started her Australian tour at the Melbourne Summer Set with a straight-sets win in qualifying against Alexandra Osborne, before withdrawing due to injury in the next round. At Adelaide, she lost in the first round to Maddison Inglis, in three sets. At the Australian Open, she won in the first round against Jang Su-jeong, before she defeated reigning US Open champion Emma Raducanu in three sets to reach the third round, her best result at a Grand Slam.[16] She is the first player from Montenegro to reach the third round of a Grand Slam. She was defeated in the third round by the former world number 1 Simona Halep.
Performance timelines[]
Key
W
F
SF
QF
#R
RR
Q#
P#
DNQ
A
Z#
PO
G
F-S
SF-B
NMS
P
NH
(W) Won; (F) finalist; (SF) semifinalist; (QF) quarterfinalist; (#R) rounds 4, 3, 2, 1; (RR) round-robin stage; (Q#) qualification round; (P#) preliminary round; (DNQ) did not qualify; (A) absent; (Z#) Davis/Fed Cup Zonal Group (with number indication) or (PO) play-off; (G) gold, (F-S) silver or (SF-B) bronze Olympic/Paralympic medal; a (NMS) downgraded Masters Series/1000 tournament; (P) postponed; (NH) not held. SR=strike rate (events won/competed)
To avoid confusion and double counting, these charts are updated at the conclusion of a tournament or when the player's participation has ended.
Only main-draw results in WTA Tour, Grand Slam tournaments, Fed Cup/Billie Jean King Cup and Olympic Games are included in win/loss records.[17]
^The first Premier 5 event of the year has switched back and forth between the Dubai Tennis Championships and the Qatar Total Open since 2009. Dubai was classified as a Premier 5 event from 2009–2011 before being succeeded by Doha for the 2012–2014 period. In 2015, Dubai regained its Premier 5 status while Doha was demoted to Premier status. The Premier 5 tournaments were reclassified as WTA 1000 tournaments in 2021.
^In 2014, the Toray Pan Pacific Open was downgraded to a Premier event and replaced by the Wuhan Open. The Premier 5 tournaments were reclassified as WTA 1000 tournaments in 2021.
Montenegro
Agnieszka Radwańska
Çağla Büyükakçay
Veronika Kudermetova
Stephanie Vogt
Lara Arruabarrena 
Lucie Hradecká
Elise Mertens 
Xenia Knoll
Andreea Mitu 
Vera Lapko
Monique Adamczak 
Misaki Doi
Alexa Guarachi
Dalila Jakupović
Lee Ya-hsuan 
Isabella Shinikova
Paula Ormaechea
Melanie Klaffner
Jasmina Tinjić
Pauline Parmentier
Jana Čepelová
Louisa Chirico
Richèl Hogenkamp
Corinna Dentoni 
Elina Svitolina
Laura Pigossi
Réka Luca Jani 
Oksana Kalashnikova
Wang Xinyu
Nina Stojanović
