Mirza, who has returned to grass court Grand Slam after three years, and Mattek-Sands lost 4-6 3-6 to the Russian pair of Elena Vesnina and Veronika Kudermetova in one hour and 28 minutes.
Sania will now become the first female athlete to represent India at four Olympics when she features at the Tokyo 2020, slated to get underway from July 23 while Ankita Raina will be making her debut at the showpiece event.
It was Sania's first match in 12 months and incidentally it was at the Doha Open where she played last in February 2020 before pandemic halted the tennis competitions across the world.