after the general symptoms improved, the Ministry of Health and Family Welfare said.
But the student developed a fever again on July 25 and two days later was admitted to a private clinic for treatment. She was put on a ventilator in an intensive care unit and was treated with the anti-viral drug Oseltamivir.
"Her condition deteriorated again with multi-system involvement and (she) expired on the evening of Monday," the ministry said in a statement.
The department said in the same statement three more people tested positive for swine flu in Pune -- two school-age students and a 26-year-old man who had recently returned from Frankfurt in Germany.
Four other people were confirmed as having the virus elsewhere in India on Monday -- two in the capital New Delhi, one in the southern city of Chennai and another in the western state of Gujarat.
Pune has seen a cluster of cases in recent weeks. About 90 children were affected by what was described as an "influenza-like illness" which was reported in the first week of July and several tested positive for H1N1.
A number of the students had earlier visited the United States, where swine flu emerged in April along with Mexico, while others had been in the Netherlands.
The Indian government said 2,479 people had been tested so far out of whom 558 had tested positive for H1N1. Of the 558, 470 have since been discharged.
Mumbai's top public health doctor Jairaj Thankear said in May that India was "certainly" at risk of having cases of swine flu, most likely from people bringing in the virus from abroad.
Many of India's confirmed cases involve people who have returned from abroad or those who have had contact with them.
But Thanekar said a combination of climatic and meteorological factors -- such as high temperatures and humidity -- and social factors was likely to lower the risk of transmission.
"Viruses don't thrive in those kind of conditions," he said.
Mumbai -- one of the most densely-populated places on earth -- also has few pig farms, reducing the risk of animal to human transmission. The city's 18 million people had also proved resilient to viruses in the past, he said.
Dr Sanjay Oak, who oversees the running of state hospitals in Greater Mumbai region, recalled that India was relatively spared from the 2002-2003 outbreak of Severe Acute Respiratory Syndrome (SARS).
"We didn't have SARS in Mumbai. One of the theories that was put forward was the climate and heat was probably not sustainable for the virus and it destroys itself. That could be one of the reasons," he said in May.
Nevertheless, precautionary measures have been taken, including airport screening, setting up quarantine centres and a specially-designated hospital with up to 1,000 beds to treat confirmed cases.