National coach Joachim Loew has also included goalkeeper Robert Enke and midfielder Marcell Jansen for the matches in Leipzig on March 28 and Cardiff on April 1.
Podolski has been in goal-scoring form for Bayern Munich since returning from a back problem while Friedrich remains a rock in league leaders Hertha Berlin's defence after a brief injury break.
"It is good that Lukas again plays a good role at Bayern," Loew said. "But we would have called him up anyway because he is a valuable striker, who we trust very much."
Both Podolski and Friedrich missed Germany's 1-0 home defeat against Norway in a friendly last month.
Loew surprisingly dropped Werder Bremen midfielder Ozil, who has been a regular for his club.
Ozil had also been courted by Turkey because of his family's roots.
As expected, injured striker Miroslav Klose was not included in the squad.
Germany are top of Europe Group Four with 10 points from four matches, four ahead of Russia who have a game in hand.
Squad:
Goalkeepers: Rene Adler (Bayer Leverkusen), Robert Enke (Hanover 96), Tim Wiese (Werder Bremen);
Defence: Andreas Beck (1899 Hoffenheim), Arne Friedrich (Hertha Berlin), Andreas Hinkel (Celtic) Philipp Lahm (Bayern Munich), Per Mertesacker (Werder Bremen), Serdar Tasci (VfB Stuttgart), Heiko Westermann (Schalke 04), Marcel Schaefer (VfL Wolfsburg)
Midfield: Michael Ballack (Chelsea), Torsten Frings (Werder Bremen), Thomas Hitzlsperger (VfB Stuttgart), Marko Marin (Borussia Moenchengladbach), Simon Rolfes (Bayer Leverkusen), Bastian Schweinsteiger (Bayern Munich), Marcell Jansen (Hamburg SV), Piotr Trochowski (Hamburg SV)
Strikers: Mario Gomez (VfB Stuttgart), Patrick Helmes (Bayer Leverkusen), Stefan Kiessling (Bayer Leverkusen), Lukas Podolski (Bayern Munich).
