Half of the deaths have been reported from the western state of Maharashtra. Rajasthan, Andhra Pradesh and Karnataka have also reported deaths.
Nearly 130 others have been infected with the virus, and many of them admitted to hospitals.
The cause of the sudden outbreak is not clear. The virus killed more than 450 Indians when it first emerged in 2009.
“The health ministry is monitoring the situation and there is no cause for worry. The states where cases had been reported have been advised to step up surveillance to control the further spread of the virus,” Health Secretary PK Pradhan told the Press Trust of India news agency.
The media in Pune has been carrying reports about swine flu patients being admitted to local hospitals.
“There is no panic, but fresh patients are being brought to the hospitals every day,” a local journalist said.
More than 450 people died of swine flu in India when it first broke out in 2009.
More than 13,000 people were infected with the virus during that outbreak.
The virus is thought to have killed more than 1,200 people around the world.
The swine flu (H1N1) virus first emerged in Mexico in April 2009 and has since spread to many countries.