"I have decided not to join the Davis Cup team to Kazakhstan," the world number three said on his website (www.rogerfederer.com).
"I need some extra time to relax after the intense weeks in North America so I can finish the year strongly."
Switzerland, beaten 4-1 by Spain in the first round this year, need to win the tie to play in the World Group next season.
Federer, beaten by Novak Djokovic in the semi-finals at the U.S. Open, has played 48 Davis Cup rubbers, including doubles, and won 37.
Stanislas Wawrinka, Marco Chiudinelli, Michael Lammer and Yves Allegro will make up the Swiss team.
"Of course, we would have liked to have had Roger for this match, but we were prepared for this possibility," team captain Severin Luethi told Swiss media. "But I'm happy that Stanislas is in such excellent form."
(Reporting by Brian Homewood; Editing by Ken Ferris)