"I spoke to Djokovic last night and he said he will not be coming to India," Obradovic was quoted as saying by the Press Trust of India in the southern Indian city where the tie opens on Friday.
Djokovic, who claimed his seventh Grand Slam title in July when he won Wimbledon, was stunned by Japan's Kei Nishikori in the US Open semi-finals on Saturday.
Serbia won the Davis Cup in 2010. But they were relegated to the playoffs for the first time since 2007 when, playing without Djokovic, they lost to Roger Federer's Switzerland in the World Group first round in February.
Djokovic's loss is a further blow to the Serbs who are already depleted by injuries to Janko Tipsarevic and Viktor Troicki. He is likely to be replaced for the tie by Ilija Bozoljac.
The 61st-ranked Dusan Lajovic, aged 24, will be the main singles player. Others in the squad are world number 107 Filip Krajinovic and doubles specialist Nenad Zimonjic.
India, hoping to return to the elite 16-nation World Group after a three-year absence, will have Somdev Devvarman and Yuki Bhambri as the two singles players.
Veteran Leander Paes and Rohan Bopanna are expected to play the doubles for the hosts.