Iran’s Deputy Health Minister Ali-Akbar Sayyari told the official IRNA news agency 28 had died in Kerman province and five in Sistan-Baluchistan.
He warned that the outbreak was likely to spread to other areas of the country, including Tehran.
Swine flu is a strain of the influenza virus known as H1N1.
The strain first appeared in Mexico in 2009 and rapidly spread around the world.
Another Iranian news agency, ISNA, reported that around 600 people had received hospital treatment after contracting the virus in Kerman province.