The 29-year-old, who arrived in the former Soviet nation on Friday, went to a doctor because he was not feeling well, the prime minister added.
"He is now in good condition," Pashinyan said, adding that authorities planned to isolate those had been in contact with him.
Armenia closed its border with Iran for two weeks and suspended air traffic a week ago. Iran is at the epicenter of the outbreak in the Middle East, with several regional nations reporting cases stemming from Iran.Neighboring Georgia and Azerbaijan reported infections this week, with three in each country.