Ivanovic, who won the French Open in 2008 to reach the top spot, has plummeted to 58th in the rankings after suffering a series of morale-crushing defeats.
"I spoke with captain Dejan Vranjes and the president of the (Serbian tennis) federation Slobodan Zivojinovic and together we decided that under these circumstances it's not the right time for me to be part of the team," Ivanovic said on her official website (www.anaivanovic.com) on Monday.
"Despite my non-presence I believe we have a good team led by Jelena (Jankovic) and this is a great opportunity for one of the young, upcoming players to play on the biggest stage.
"I know that Serbia will put up a performance of great commitment and passion as always while I will continue to make all the necessary steps to find my form."
Although she lost both her singles in a 3-2 first round defeat to Russia in Belgrade, Ivanovic's absence will seriously dent Serbia's hopes of staying in the World Group.
With only a handful of young prospects in support, world number eight Jankovic faces a mammoth task of winning both her singles and the doubles in the home tie.
Since her 2008 French Open success, Ivanovic has made a string of early exits, including at the last two grand slam events, and has not won a tournament for 16 months.
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