Third-seeded Paes and Mahesh Bhupathi, the runners-up here in 1999, lost 4-6, 6-7 (7/4) to sixth-seeded Polish duo Mariusz Fyrstenberg and Marcin Matkowski here Thursday.
India are scheduled to play Japan in Tokyo from Sep 16-18 for a place in the World Group next season. The partnership of Paes and Bhupathi for the doubles rubber is key to India's chances in the tie.
"Rough day for Leander, back spasms during the doubles. Out of mixed and now in doubt for Davis cup too," Bhupathi wrote on his Twitter account.
The loss of the "Indian Express" pairing of Leander Paes and Mahesh Bhupathi leaves Rohan Bopanna as the only Indian in the men's draw.
Bopanna and his Pakistani partner Aisam-Ul-Haq Qureshi, the runners-up here last year, were leading 7-5, 2-6, 6-5 against the English pair Colin Fleming and Ross Hutchins when play was stopped due to rain.
"Well, had to stop at 6-5 (15-30), Aisam serving in the final set due to the drizzle. But surprisingly they cancelled us for the night," Bopanna tweeted.
The fifth-seeded India-Pakistan pair will now finish their match at court 17 after the boys' singles match. If they win, they will face Fyrstenberg and Matkowski.