After beginning his career as a circuit touring cars driver, Kopecký changed to rallysport in 2001, winning the national sprintrally championships at first. In 2004, he won the national classical rally championships and entered the world championships next year.
In 2007, he continued competing with the Fabia and placed 12th in the drivers' world championship. His best finish was 5th place at the 2007 Rallye Deutschland, he scored more points than in 2006, 10 points and 12th position.
Kopecký competed in the Intercontinental Rally Challenge with a works Škoda Fabia Super 2000 finishing second in the championship and winning two events, the Rally Principe de Asturias and Barum Czech Rally Zlín, making him the first Czech driver to win the rally in a Czech car.[2] Kris Meeke became champion with Peugeot 207 S2000 in 2009.