He played his club football in Czechoslovakia, mainly for Dukla Prague, with whom he became joint top scorer of the 1960–61 Czechoslovak First League with 17 goals.

In the European Cup, Kučera scored 11 times in 14 matches,[3] ranking him third highest goalscorer overall from Czechoslovak players in the pre-Champions League era of the competition behind Jozef Adamec and Ivan Mráz.

In a 1963–64 European Cup match against Polish side Górnik Zabrze, Kučera was injured following an elbow to the head from defender Stanisław Oślizło and never played at the top level again.

[5] In total he scored three goals in seven appearances between 1961 and 1963,[3] although he missed the 1962 FIFA World Cup due to injury.

[6] Dukla Prague Individual Media related to Rudolf Kučera at Wikimedia Commons