Tourism Minister Ali Asghar Mounesan and member of the Expediency Council Mohammad Ali Iravani have also been infected with the coronavirus
Iran's senior vice president and two other cabinet members tested positive for the novel coronavirus.
The exile-run IranWire news site reported they are undergoing treatment.
According to the list, Tourism Minister Ali Asghar Mounesan and member of the Expediency Council Mohammad Ali Iravani have also been infected with the coronavirus. Iravani is also a member of Supreme Leader Ayatollah Ali Khamenei's office, reported Al Jazeera.
Hossein Mohammadi, another member of Khamenei's office, could also be infected with coronavirus, local news website Saham News had reported.
Five members of Iran's Islamic Revolutionary Guard Corps (IRGC) have died from coronavirus, IRGC spokesman Ramezan Sharif said on Wednesday, reported Al Arabiya.
At least 13 Iranian regime figures have died from coronavirus and 11 others were infected since the beginning of the outbreak in the Islamic Republic.
Iran is among the world nations hardest-hit by the virus.
The death toll in Iran from the new coronavirus climbed for another consecutive day, killing 62 more people in the past 24 hours as the government on Wednesday raised the nationwide death toll to 354.
Iran's health ministry said the deaths are among some 9,000 confirmed cases in Iran, where the virus has spread to all of the country's 31 provinces.
Across the Middle East, the vast majority of the 9,700 people who have contracted the coronavirus or the COVID-19 illness that it causes are in hard-hit Iran or had recently returned from there.
The Islamic Republic has one of the world's worst death tolls outside of China, the epicentre of the outbreak. Outside of Iran, only Iraq, Egypt and Lebanon have recorded deaths from the virus in the Middle East.
There are concerns that the number of infections across Iran is much higher than confirmed cases reported by the government, which is struggling to contain the outbreak's spread. The rising casualty figures each day in Iran suggest the fight against the new coronavirus is far from over.
Among the dead are five of Iran's elite Islamic Revolutionary Guard Corps members and an unspecified number of the Guard's volunteer Basij force.
Iran's supreme leader said on Tuesday that the Islamic Republic will recognise doctors and nurses who die combating the new coronavirus as "martyrs".
The decision by Supreme Leader Ayatollah Ali Khamenei comes amid a propaganda campaign already trying to link the fight against the virus to Iran's long, bloody 1980s war with Iraq. Its forces, which include virologists, faced chemical weapons during Iran's eight-year war against Iraq during Saddam Hussein's regime.