On 6 April 2015, she reached her best singles ranking of world number 57. On 19 May 2014, she peaked at world number 184 in the doubles rankings. In June 2013, Smitková made her Women's Tennis Association tour main draw debut at the Nürnberger Versicherungscup.
After coming through all three qualifying rounds, she lost to Julia Cohen in round one.
A year later, she reached the third round of qualifying at the 2014 French Open, defeating 17th seed Victoria Duval in the first round and former top-20 player Anabel Medina Garrigues in the second. She lost in the third and final round of qualifying to fifth seed Danka Kovinić.
In the qualifying tournament for Wimbledon in June 2014, Smitková again reached the third round, this time defeating Madison Brengle in three sets to seal her maiden Grand Slam main draw appearance. In the third round, she defeated Bojana Jovanovski, in a match where Jovanovski served for the match twice and had held a match point on Smitková"s serve.
Her run was over in round four after losing to fellow Czechoslovakian Lucie Šafářová in straight sets.
Women's Tennis Association 125K series finals
= Singles (1–0)