Štěch was capped at under-17 and under-21 levels for the Czech Republic. He made his under-17 debut in a 1–0 win against Finland in February 2006, and played in the 2006 UEFA European Under-17 Championship as the Czech Republic finished the competition as runners-up to Russia. Štěch made his under-21 debut in a friendly against South Korea in March 2009, and was named in the Czech Republic's squad for the 2011 UEFA European Under-21 Championship, which they finished in fourth place.