Paes is locked in a legal battle with his partner Rhea Pillai for the custody of their daughter and one of the hearings of the case would be around the tie, scheduled for September 12-14 in Bangalore.
"Leander will play Asian Games and was very much willing to play in the Davis Cup as well. However due to his personal compulsions, AITA has decided to accept his request to not play against Serbia," AITA Secretary General Bharat Oza said.
Later Paes had said that he was available for national duty if required. He had missed the Asia/Oceania Group I ties against Chinese Taipei and Korea also.
World number two Serbia are expected to arrive without world No. 1 Novak Djokovic but they have formidable doubles players such as Nenad Zimonjic in their ranks.