In 2003 he moved to the Czech Republic to Banik Ostrava. There he was in season 2003/ 04 Czech scorer and Czech champion.
In the summer of 2004, he was obliged by Borussia Mönchengladbach, after he had performed well in the Czech national team and scored two goals at the European Championships in Portugal. However, Marek Heinz could not meet the expectations.
In the summer of 2005, the Czech moved for 2.2 million € to Galatasaray. Even with Galatasaray Marek Heinz rather disappointed and achieved there in 13 inserts only three goals.
Since September 2006, Heinz played at the traditional club AS Saint- Étienne in the French Ligue 1, but where he could not convince. End of August 2007 changed Heinz for French second division club FC Nantes. On 30 September 2008, he announced his existing contract with FC Nantes and moved to his home to FC Brno. At the beginning of the season 2009/10 changed the Czech in the Austrian Bundesliga Kapfenberg SV. In summer 2010, Heinz joined Ferencvaros Budapest. A year later he returned to his Czech home to Sigma Olomouc.
For the Czech national Heinz played 30 games and scored five goals. At the European Championships in Portugal in 2004, he was instrumental in the departure of the German national football team in the first round by in the third group game the score to 1:1 achieved ( Result: 2-1 for the Czech Republic ).