Nehwal defeated former world champion Thailand's Ratchanok Intanon 21-16, 21-14 in the final at the Siri Fort Indoor Complex.
Gandhi said that Saina was an inspiration to millions of people.
"I join our country men and women in expressing pride and delight at your tremendous achievement- You have shown that Indians are second to none if we put our minds to it.
"You are an example to millions of our young girls and boys who dream of excellence and success," said Gandhi.
Earlier on Sunday, Kidambi Srikanth won the men's singles title at the same tournament, battling past sixth seed Axelsen 18-21 21-13 21-12 in a gruelling contest.