The Islamic republic has been battling to control an outbreak of the novel coronavirus that has claimed 19 lives among 139 infections in the past week.
"Twenty-four people were arrested and handed over to the judiciary and 118 (internet) users were talked to and let go" after receiving warnings, said Vahid Majid, head of the Iranian police force's cyber unit.
The arrests were carried out after the establishment of a special unit to "combat rumour-mongers regarding the 'spread of coronavirus in the country'," he was quoted as saying.
"The police are monitoring all the news published in the country's cyberspace."
Majid said the unit would take action over news, pictures or videos that "contain rumours or fake news meant to disturb the public and increase concern in society".