Alexander Stolz started his career with SV Sandhausen, before joining Regionalliga club FC Nöttingen for a year in 2004. A spell at VfB Stuttgart followed between 2005 and 2012. It was during this period that Stolz first played for TSG Hoffenheim, the shot-stopper joining the Kraichgau club on loan for the 2006/07 campaign. He terminated his contract with VfB Stuttgart in 2012 and moved to Karlsruher SC. He returned to Hoffenheim in 2013 and has since made one competitive appearance. In the summer of 2019, the goalkeeper extended his contract for another year.