Kwak had 1 top ten in each of her three seasons on the Futures Tour, with her best finish being a tie for third in 2011. She entered 2011 LPGA Qualifying School and finished tied for 20th to earn limited status on the LPGA for 2012.

Kwak only made one cut in seven LPGA events played in 2012. She also played on the Symetra Tour, but only finished 113th on that tour's money list. Fortunately, she finished tied for 32nd at Q-School in December to earn Category 17 status for 2013.

Kwak only made one cut in 2013, however, and barely made more money that season than she had in 2012. She did not regain a card at Q-School and played on the Symetra tour in 2014. Fortunately, she did quite well on that tour, finishing second on the money list thanks to 7 top tens and 2 wins. She thus earned back a full tour card on the LPGA for 2015.

Min Seo had by far her best season on tour in 2015. Although she still missed more cuts than she made, she had two of her best ever finishes on the LPGA. At the Swinging Skirts in April, she managed a solo 4th place despite shooting a final round 74. At the Meijer Classic, she produced her best ever score, a 65, en route to a tie for 13th. Thus, she made $165K for the year, roughly 20 times her next best season, and finished 76th on the money list. For the first time, she earned a category 1 status on tour!

Kwak started out her 2016 season well by notching two top tens in her first three starts: a tie for 8th at the Pure Silk Bahamas, and a tie for 4th, her best yet finish, at the Australian Women's Open. After that, however, she missed the cut at most of the rest of the events she played. She wound up earning $117,459, which put her 92nd on the money list. Her status slipped to category 11 for 2017.

Kwak only made $23,000 on the LPGA tour in 2017, finishing 151st on the money list, and so lost her playing privileges for 2018. In 2018 and 2019, she played on the Symetra Tour, trying to regain her tour card for the LPGA.

Finally, she earned her LPGA card back at 2019 Q-Series by finishing in the top 45 on the leaderboard.

In 2020, the whole world was rocked by the Covid-19 pandemic. The LPGA and KLPGA tours canceled and postponed many tournaments. Min Seo Kwak ended up playing just seven LPGA events during the year, missing four cuts. Her best finish was a tie for 28th. She made just a little over $16,000, but fortunately for her, the LPGA decided to allow all players to keep their cards until the end of 2021 because of the pandemic.

In 2021, Kwak had a weak season. She made just 5 cuts in 15 events, with her best finish a t-17th at the ISPS World Invitational. She earned just a little less than $34,000, 126th on the money list. She was not able to improve her ranking at Q-Series, missing the cut there; so she entered 2022 with a category 18 status.

In 2022, Kwak played four events on the LPGA but missed all the cuts. She returned to the Symetra tour in 2023 but was not able to regain her LPGA tour card for 2024.