Dudka began his career at hometown club Celuloza Kostrzyn, before moving to Amica Wronki. He made his debut for Amica Wronki in the Ekstraklasa on 4 April 2000. In 2005, he moved to Wisla Kraków, where he made 77 league appearances. In June 2008, he joined Ligue 1 side Auxerre. After four seasons he moved to Levante on a free transfer.
After a trial, Dudka signed a two-month contract with English Championship club Birmingham City on 31 October 2013. He made two appearances, the last on 7 December, was reportedly surprised at the pace of the game in the Championship, and left the club when his contract expired.