Schwaab began his career with SC Freiburg in the 2. Bundesliga. In his second season with the first team, he started in every single match that he played. Overall, he scored six league goals for Freiburg despite being a defender.
After the end of his contract with Leverkusen on 1 July 2013, Schwaab moved to VfB Stuttgart on a free transfer. On 8 May 2013, Daniel Schwaab signed a contract until June 2016 with VfB Stuttgart. He made his debut with VfB Stuttgart on 17 August 2013, against his previous team Bayer Leverkusen, where he scored an own goal. The match ended 0-1, with Stuttgart losing the game.
A youth international since the U-18 level, Schwaab was called up to the U-21 side for the 2009 European Championships and won the title. He made only one appearance, as a substitute during the final, at the tournament but soon became first choice for the new qualifying campaign.