Lukas Rosol is expected to move up to the number two spot while Ivo Minar will be added to the squad.
"I cannot take part with the guys, unfortunately I have a problem with my disc that I have to have an operation on," Stepanek said in a video on the team's Facebook page.
Stepanek, 34, and world number six Tomas Berdych led the Czechs to their first Davis Cup title as an independent nation in November.
Stepanek's gruelling four-set victory over Spain's Nicolas Almagro clinched the title for the host nation.
The Czech team will start its 2013 campaign in Geneva against a Swiss team that will be without world number two Roger Federer.