Sania will partner Canada's Daniel Nestor while Bhupathi will team up with America's Liezel Huber.
Sania and Nestor are unseeded while Bhupathi-Huber are the top seeds.
Defending champions, India's Leander Paes and Zimbabwe's Cara Black are second seeds.
"Sania's wrist has been hurting on and off over the last few weeks and she was not sure whether she would play the mixed doubles event. She wanted to decide at the last moment after gauging the condition of her injury.
"Under the circumstances, we thought it would not be fair on Mahesh as he could end up missing out on the event if Sania was forced to back out at the last moment.
"Hence, it was mutually decided that he would finalise another partner for himself and in case Sania decided to play in the mixed at the last moment, she would try to find someone who was still available," Imran Mirza, Sania's father, said.
Nestor and Zimonjic win Wimbledon doubles title
Sania-Chuang through to Madrid semis
Sania-Chuang fall in semis
Paes-Black cruise into final at Wimbledon
American duo claim mixed doubles crown