Schwarz played junior in his native Czechoslovakian Republic with Sparta Praha"s junior team He made his debut at the senior level with Sparta Praha playing one game in the Czechoslovakian Extraliga in 2002-2003. The following season, he joined the Extraliga full-time at seventeen-years-old and played between three teams – The Human Context Plzeň, The Human Context Oceláři Třinec and Sparta Praha.
That off-season, Schwarz was drafted 17th overall by the Saint Louis Blues in the 2004 National Hockey League Entry Draft.
Upon being drafted, he moved to North America to play major junior in the Western Hockey League (WHL) with the Vancouver Giants. He posted a 2.67 Gaelic Athletic Association and a winning record before moving back to the Czechoslovakian Republic the following season to continue to play for Sparta Praha.
In 2006-2007, he began playing for the Peoria Rivermen, the Blues" American Hockey League (AHL) affiliate. He was called up that season and played in his first National Hockey League game on December 12, 2006, against the Chicago Blackhawks.
Schwarz made 21 saves on 24 shots as the Blues lost 3–2.
At 20 years old, he became the third youngest goaltender in Blues history to play in a game. On October 25, 2008, Schwarz combined with third-string goalie Ben Bishop for a 4-0 shutout against the Florida Panthers. With Manny Legacé and Chris Mason out due to injuries, Schwarz was called up to play backup to Bishop when Bishop also went down with an injury in the third period.
Schwarz completed the shutout with 15 minutes to go.