Saina, who clinched her second Australian Open title earlier this month, exchanged places with Japan's Nozomi Okuhara, who now occupies the sixth spot in the women's singles list headed by Spain's Carolina Marin.
Sindhu, on the other hand, remained static at 10th.
In the men's singles rankings, Srikanth Kidambi, Ajay Jayaram and H S Prannoy were unchanged at 11th, 24th and 28th respectively. Sameer Verma gained one place to move up to 36th while B Sai Praneeth slipped four places to be at 37th.
In the men's doubles Manu Attri and B Sumeeth Reddy also slipped two places to occupy 23rd spot while the young pair of Pranaav Jerry Chopra and Akshay Dewalkar moved up one spot to be at 29th.
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