Early career As a youth player, Heinz played for such Czech football clubs as Lokomotiva Hodolany,
Olomouc-Holice and
Sigma MŽ Olomouc. Although he trained as a
car mechanic and considered becoming involved in
natural science, Heinz went into professional football, playing for Sigma Olomouc with a short loan spell at
Lázně Bohdaneč before moving to Germany in 2000. Bielefeld were relegated from the
Bundesliga after losing their final game of the season in May 2003.
Baník Ostrava signed Heinz from the Hamburg club ahead of the 2003–04 season. He made his debut for the club in July 2003, providing two
assists in a win against
České Budějovice. Heinz scored his first Baník goal in a 1–1 draw against
Liberec just a week into the season, He formed a partnership with
Miroslav Matušovič which returned 29 goals for the club that season.
Second stint in Germany and Turkey (2004–2006) After
Euro 2004 Heinz returned to Germany, signing for
Borussia Mönchengladbach at the start of the
2004–05 season. He scored his first and ultimately only Bundesliga goal for Gladbach in a 3–1 victory against
Werder Bremen. Heinz played 14 matches in the first half of the season but was demoted to the amateur reserve side in March 2005 after the club appointed
Dick Advocaat as head coach mid-season. A proposed move back to the Czech Republic to play for
Sparta Prague fell through the same month after the involved clubs were unable to agree on a transfer fee. He left Borussia Mönchengladbach in August 2005, having made 23 Bundesliga appearances and scored one goal. In September 2005, Heinz joined Turkish side
Galatasaray on a three-year contract. Following its victory in the
2005–06 Süper Lig, Heinz left the club on 31 August 2006 and became a free agent.
France and third stint in the Czech Republic (2006–2009) In September 2006, Heinz signed a one-year contract with French side
Saint-Étienne to play under Czech head coach
Ivan Hašek. In a 2–0 win against
Lorient in early December, Heinz scored a left-footed free-kick from 18 metres, with the ball finishing in the goalkeeper's top-left corner. It was shortlisted as one of the five best goals of matchday 16. He scored 4 goals in 28
Ligue 1 matches for Saint-Étienne but left the club after Hašek was replaced as head coach by
Laurent Roussey. On 21 August 2007, Heinz signed with another French club
Nantes to play in the
2007–08 Ligue 2. He scored in the third round of the
2007–08 Coupe de la Ligue against
Monaco, although a 2–0 half time lead was not enough as Monaco secured the win and progression to the fourth round with three second-half goals. Heinz played a total of 16 league matches, scoring once, as Nantes achieved promotion to the French top flight. On 30 September 2008, Heinz returned the Czech league, signing a two-year contract with
Brno. He scored his first league goal for Brno with a header in a 2–0 win against Banik Ostrava on 22 February 2009. He left the club after a single season, having scored two league goals in 21 appearances.
Austria and Hungary (2009–2011) On 29 June 2009 it was announced that Heinz had signed a one-year contract with
Kapfenberger SV to play in the
2009–10 Austrian Football Bundesliga. Heinz was suspended for three matches in February 2010 for being verbally abusive after a 4–3 loss against
Austria Vienna. He left the club as his contract expired after the season. Heinz moved to his fifth foreign country to play football in July 2010, signing a one-year deal with Hungarian side
Ferencváros. He made his debut for the club in the opening game of the
2010–11 Nemzeti Bajnokság I season, a 2–1 win against
Paks, scoring a follow-up shot after his initial shot was blocked. Heinz scored 7 goals in 25 league appearances for the club, receiving a first-half
red card in a 6–0
Derbi loss against
Újpest as well as another red card in his final match for the club, which was against
Szombathelyi Haladás.
Return to Olomouc and Znojmo (2011–2013) Heinz returned to Olomouc in 2011, signing a two-year contract. Despite playing 20 matches in his first season, Heinz played just seventeen minutes in one substitute appearance in the first half of his second season. In November 2012, manager
Roman Pivarník announced Heinz was surplus to requirements and free to find another club. He joined second league
1. SC Znojmo on loan in January 2013 for the rest of the season. In his league debut for Znojmo at the start of March 2013, Heinz scored a hat trick against
Karvina in a 3–0 win. His opening goal came after 10 minutes with a successful shot from less than 20 metres from goal. In the 17th minute Heinz made it 2–0 with a curling shot over the goalkeeper's head and the scoring was complete in the 49th minute when he
nutmegged the goalkeeper. On 23 March Znojmo defeated
Bohemians 1905 2–0 with goals from Heinz and
Radim Nepožitek, lifting the side to first place in the Second League table. Heinz contributed 8 goals in 12 league matches. helping Znojmo finish the season top of the league to win promotion to the Czech First League for the
2013–14 season. Znojmo became the third Czech First League club that employed Heinz. In the 2013–14 season match played on 17 August he was one of two players, alongside fellow player
Jan Kopic, to score twice in a 5–5 draw away at Jablonec. In September 2013, after Znojmo started with nine consecutive winless games, Heinz agreed to part ways with the club. ==International career==