The Hannover striker did not play in any of Germany's qualifying games and has just the one cap to his name - after making his debut against USA in March 2002.
Voller has opted to leave a place in the squad open - which will be filled by June 2 - allowing an Under-21 player to make the trip.
Bayern Munich's talented midfielder Bastian Schweinsteiger and Cologne striker Lukas Podolski are the favourites to pinch the final spot.
Brdaric's call-up has meant Bayer Leverkusen's Oliver Neuville, who is to join Borussia Monchengladbach in the summer, is left out.
"Oliver hasn't been on form over the last few weeks and has been sitting on the bench at Leverkusen," said Voller. "Thomas has been scoring goals and so earned his chance."
Voller retains a strong midfield, with the likes of Michael Ballack, Torsten Frings and Dietmar Hamann all included, although he is without Carsten Ramelow who has retired from international football.
Timo Hildebrand has been named as the third choice keeper behind the Oliver Kahn and Jens Lehmann, while Andreas Hinkel has returned just in time from injury to make the squad.
Germany will now refine their starting XI ahead of their opening Euro 2004 clash against Holland on June 15 with warm-up games against Malta, Switzerland and Hungary.
Full squad: Oliver Kahn (Bayern Munich), Jens Lehmann, (Arsenal), Timo Hildebrand (Stuttgart); Frank Baumann (Werder Bremen), Arne Friedrich (Hertha Berlin), Andreas Hinkel (Stuttgart), Philipp Lahm (Stuttgart), Jens Nowotny (Bayer Leverkusen), Christian Worns (Borussia Dortmund), Christian Rahn (Hamburg); Michael Ballack (Bayern Munich), Fabian Ernst (Werder Bremen), Paul Freier (Bochum), Torsten Frings (Borussia Dortmund), Dietmar Hamann (Liverpool, England), Jens Jeremies (Bayern Munich), Sebastian Kehl (Borussia Dortmund), Bernd Schneider (Bayer Leverkusen); Fredi Bobic (Hertha Berlin), Thomas Brdaric (Hannover 96), Kevin Kuranyi (Stuttgart), Miroslav Klose (Kaiserslautern).
