He plays midfield and defence. He previously played for Sigma Olomouc, Sparta Prague, Spartak Moscow, West Ham United, Football Club Basel and Slovan Liberec. On 6 January 2010, he announced his retirement from international football after representing the Czechoslovakian Republic U21 and the senior team for nine years.
Having come through the ranks of Sigma Olomouc, Kováč joined Sparta Prague in 2004.
In July 2005, he moved to Russia, where he signed for Spartak Moscow. During a Moscow derby against Lokomotiv Moscow on 20 July 2008, Kováč received a yellow card for tackling a fan who invaded the pitch.
West Ham United
On 30 January 2009, he moved on loan to West Ham United for the remainder of the 2008-2009 season. He made his debut for West Ham on 25 February 2009 in a 2–0 FA Cup defeat to Middlesbrough.
His first goal for West Ham came in their 3–1 away defeat to Everton on 16 May 2009.
Kováč signed a permanent contract with West Ham United on 11 August 2009 on a three-year contract. At the end of the 2010/2011 season, with twelve months left on his contract and after 62 league and cup appearances, Kováč left West Ham United. Basel
In July 2011 Kováč joined reigning Swiss Super League champions F.C. Basel for an undisclosed fee on a two-year contract.
He made his debut for his new club on 16 July 2011 in the Stade de Suisse, Wankdorf in the 1–1 away draw against Bachelor of Science Young Boys.
Kováč scored his first goal for Basel in the 1–1 away draw against Sion on 4 August 2012. Kováč appeared for his nation in the 2006 World Cup and Euro 2008.
With the Czechoslovakian Republic failing to qualify for the 2010 World Cup, Kováč announced his retirement from international football in January 2010, in order to focus on his club career. International goals
Scores and results list Czechoslovakian Republic"s goal tally first.