Former champion and 2012 Olympic bronze medalist Saina suffered a 17-21 9-21 straight game loss to compatriot Malvika Bansod.
Malvika, ranked 111th, took 34 minutes to see off the former world number 1.
Earlier, the top seed Sindhu had no problem dispatching fellow India Ira Sharma 21-10 21-10.
She will meet compatriot Ashmita Chaliha, who got the better of French shuttler Yaelle Hoyaux 21-17 21-14, in the quarterfinal.
Malvika will next take on fellow Indian Aakarshi Kashyap in the quarterfinals.
Aakarshi had defeated compatriot Keyura Mopatin 21-10 21-10 in another women’s singles second round match.
Prannoy received a walkover as his opponent Mithun Manjunath withdrew from the tournament after testing positive for COVID-19.
The men’s top seed Kidambi Srikanth, doubles player Ashwini Ponnappa, Ritika Rahul Thakar, Treesa Jolly, Simran Aman Singh and Khushi Gupta are the other players who had to withdraw from the tournament due to the positive COVID-19 results, which led to several walkovers.
Prannoy will meet the winner of the second round clash between third seed Lakshay Sen and Felix Burstedt of Sweden.
Sameer Verma’s campaign also came to an end in the men’s singles as he retired midway during his second-round match against Brain Yang of Canada due to calf strain. (Inputs: Agencies, NGB)