Kučová, who prefers clay courts, started tennis at the age of six. Her younger sister Kristína Kučová also became a professional tennis player.
Zuzana Kučová won eight singles and four doubles titles at tournaments of the ITF Women's Circuit with various partners . She barely missed a place in the top 100 when she reached position 101 in the individual world rankings in June 2010 .
Starting in October 2011, she was sidelined for a year and a half because of a persistent tendon injury. As a result, she fell out of the ranking in both singles and doubles. At the WTA tournament in Stuttgart she made her comeback in April 2013, but did not get beyond qualification. At the French Open she defeated Julia Görges 7: 6, 6: 0 in round one , before she was eliminated in three sets by Virginie Razzano . It was her first victory in the main draw of a Grand Slam tournament . After the greatest success of her professional career, she said goodbye to the women's tour.