Career
He is the elder brother of Hull City and Slovakia goalkeeper Dušan Kuciak. Martin Kuciak is a product of Žilina youth academy. MŠK Rimavská Sobota
After a spell at Kysucké Nové Mesto, Kuciak joined Rimavská Sobota in summer 2005, who had been relegated from the Slovak top flight the previous season.
He became the number one goalkeeper at the club in the spring part of the 2007-2008 season.
Football Club ViOn Zlaté Moravce
Kuciak transferred to the Corgoň liga club Football Club ViOn in the winter break of the 2009-2010 season. In the following four and a half years at Zlaté Moravce, he played in every single competitive game.
Despite his success at the club, Kuciak decided not to renew his contract and left Zlaté Moravce after it expired in summer 2014. Football Club Hradec Králové
Shortly afterwards, Kuciak signed for the Synot liga club Football Club Hradec Králové.
He made his debut for Hradec Králové in a 1-0 league loss to Příbram on 4 October 2014.
He was mostly used as a back-up goalkeeper behind Tomáš Koubek. Kuciak was relegated with the club at the end of the season. FO ŽP Šport Podbrezová
Kuciak came to Podbrezová in the summer of 2015.
He made his competitive debut for the club in a 2-0 league loss to AS Trenčín on 25 July 2015.