Velayati, 75, is the president of Masih Daneshvari Hospital in Tehran, and contracted the virus after being exposed to infected patients at the hospital, which is the main centre for treating COVID-19 patients.
Doctors have confirmed that Velayati, who is a paediatrician, was put into quarantine and have described his condition as "good" as he suffers only with mild symptoms.
Velayati is not the first Iranian official who tested positive for the coronavirus.
Meanwhile, an Iranian medical official was reported by the official Iranian news agency, IRNA, stating that 81 Iranians have died due to consuming toxic alcohol amid misinformation that it can cure the virus. The World Health Organisation have denied these claims.