She died in Pune. On Saturday, housemaker Fahmida Paanwala, 53, succumbed to her infection in Mumbai's Kasturba Hospital.
Authorities are closely monitoring the condition of three others - a medico and a pharmacist, who are in critical condition in Pune, and a 28-year-old businessman who is in critical condition in a Mumbai hospital.
There are 13 positive cases of swine flu in Ahmedabad. The blood samples of another 53 patients are under examination across Gujarat.
Maharashtra Chief Minister Ashok Chavan has convened an early meeting of officials and experts as a high level team of the National Centre for Disease Control, earlier known as the National Institute of Communicable Disease, left for Pune, the worst hit city, to study the situation.
Pune is in the grip of panic as thousands besiege government hospitals to get themselves checked and to take the Tamiflu medicines - if needed.
In New Delhi, the Sanskriti School, a private institution, said it was closing for a week after two of its students tested positive for swine flu Saturday.
India has reported a total of 783 cases including four deaths. Of this, over 500 patients have been cured. The most badly hit states are Delhi and Maharashtra.
Meanwhile, experts and health officials came out against moves to sell Tamiflu medicines in the open market, warning it could lead to panic buying, hoarding and even spurious sale of the anti-influenza medicine.
Randeep Guleria, head of medicine at the All India Institute of Medical Sciences (AIIMS) in New Delhi, said: 'I don't think it will be a good move. Also, overuse would develop resistance to Tamiflu and it would no longer be effective in the long run.'
Mexico, the first country to report swine flu, found that many people have developed resistance to Tamiflu.
Guleria added: 'The epidemic is here to stay for some time.'