Heinz started his football career in his native Czech Republic, where he played for Lázně Bohdaneč and Sigma Olomouc before moving to Germany in 2000.

Heinz headed to German side Hamburger SV in 2000, the same year making his first appearance for the senior team of the Czech Republic.

He first helped Galatasaray to a 4–1 win over rivals Trabzonspor in October, before he scored the all-important third goal against Finland which sent the Czechs into the 2006 World Cup held in Germany.

In September 2006, he signed a one-year contract with French side Saint-Étienne after being released by Galatasaray, hoping to finally making an impact at club level outside the Czech Republic.

After only one season Heinz left Brno, and on 29 June 2009 it was announced that he signed a one-year contract with Kapfenberger SV.