Sania and her Spanish partner Virginia Ruano Pascual were handed a 4-6 3-6 defeat by the seventh-seeded Russian-Italian combination of Alisa Kleybanova and Francesca Schiavone.
There was more disappointment for India in the junior competition with Rishika Sunkara losing 4-6 2-6 to Japan's Miyu Kato in the girls' singles opening round.
In boys' singles, Vaidik Munshaw went down 4-6 5-7 (5) to Belgian Arthur De Greef.
On Monday Indian hopes would rest on Leander Paes who will play his pre-quarterfinal match on the men's doubles competition. Paes and his Czech partner Lukas Dlouhy, seeded third, will take on unseeded Americans John Isner and Sam Querrey.
later in the day, Paes will team up with Zimbabwean Cara Black to take on the Uzbek-South African pair of Akgul Amanmuradova and Rik De Voest in the mixed doubles second round.
In the juniors' event, Rishika will team up with Japan's Yuki Ito in girls' doubles competition against the sixth seeded German-Dane duo of Anna-Lena Friedsam Mai Grage.
Vaidik Munshaw will pair up with China's Chuhan Wang in the boys' doubles and the duo will open against fourth seeds Liang-Chi Huang of Taipei and Yasutaka Uchiyama of Japan.