Two-time Olympic medallist PV Sindhu and HS Prannoy advanced to the quarterfinals but Sania Nehwal's campaign ended at the India Open on Thursday.
Former champion and 2012 Olympic bronze medallist Saina suffered a 17-21 9-21 straight game loss to compatriot Malvika Bansod. Ranked 111th, Malvika 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. In the quarters, she will meet compatriot Ashmita Chaliha, who got the better of France's Yaelle Hoyaux 21-17 21-14.
Malvika will next take on fellow Indian Aakarshi Kashyap in the quarterfinals. Aakarshi had defeated compatriot Keyura Mopatin 21-10 21-10 in their 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 Thkar, Treesa Jolly, Simran Aman Singh and Khushi Gupta also 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 Lakshya 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 a calf strain.