The 70-year-old woman fell ill while visiting the western state of Rajasthan, a popular tourist destination that has been particularly hard hit by the latest outbreak.
"She died in hospital," the chief medical officer for the Rajasthani city of Jodhpur Y. S. Rathore told AFP.
"She tested positive for the H1N1 virus," he said, referring to the swine flu virus.
The woman, whose full name has not been given, was visiting the state with a large tour group when she complained of flu-like symptoms and was admitted to a private hospital, where she was placed on a ventilator.
The postmortem report into her death will be completed later Thursday, Jodhpur police commissioner Ashok Rathore told AFP.
No one at the Swiss embassy could immediately be reached for comment.
India's health ministry said Wednesday that 407 people had died of swine flu since the start of the year, more than half of them in the first ten days of this month.
More than 5,000 cases of the disease have been detected, the ministry said.
The government said it was reviewing procedures to prevent the disease from spreading further, including vaccinating medical staff working with affected patients.
Authorities in Rajasthan, where 117 people have died, have cancelled all leave for doctors, while in neighbouring Gujarat state, panicked patients have been seen queueing outside hospitals for screening.
The Geneva-based World Health Organization declared the swine flu pandemic over in August 2010, more than a year after the H1N1 virus that emerged from Mexico sparked panic and killed thousands of people around the world.