Sandeep Dayne, 35, died on Friday night at a private hospital, where he had been undergoing treatment since August 28.
Meanwhile, six fresh cases of the viral infection have been detected in the city, which has been worst hit by the pandemic.
The Pune branch of the Indian Medical Association has announced that it would hold workshops to train doctors in rural areas to handle suspected swine flu cases.
View: The flu, the scare and the confusion
Everything you need to know about swine flu
WHO declares swine flu pandemic
New wave of deadly H1N1 is ready to explode
Nagpur admn to send medical teams for relief work