Kováč played both in midfield and in defence for Sigma Olomouc, Sparta Prague, Spartak Moscow, West Ham United, FC Basel and Slovan Liberec.

In July 2011 Kováč joined reigning Swiss Super League champions FC Basel for an undisclosed fee on a two-year contract.

To the beginning of their 2011–12 season Kováč was a member of the Basel team that won the 2011 Uhrencup, beating both Hertha Berlin 3–0 and West Ham United 2–1 to lead the table on goal difference above Young Boys.

[13] Kováč scored his first goal for the club on 4 August 2012 in the away game in the Stade Tourbillon as Basel played a 1–1 draw with Sion.

With the Czech 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.

In June 2020, he was hired as SFC Opava football manager replacing sacked Jiří Balcárek.

[20][21] In June 2022 he was hired as FC MAS Táborsko football manager replacing Sergejs Golubevs.