In recent weeks reports suggested some ministers were active on Facebook, but the ministers denied they have any social media accounts, Mohseni-Ejeie said, cited by IRNA news agency.
An investigation was launched and a man was arrested for having opened "these fake accounts, and he is now in prison," the spokesman added.
The man's identity was not immediately known nor was it clear how he managed to open the accounts as access to social media websites is blocked by the Iranian authorities.
Iran blocks access to such networks, as well as political blogs and pornography sites, to stop people from surfing content that might be immoral or undermine the Islamic regime.
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The authorities provide some private or state-owned companies a "national VPN" service which allows them to access to the world wide web.
On September 17, however, Facebook and Twitter became briefly accessible due to what an Iranian official said was a "technical glitch".
According to official figures, of the total population of 75 million in Iran, more than 30 million people use Internet.