The ministry said on its official Twitter account that the individual, who is in quarantine in hospital, had not disclosed his visit to Iran when entering Saudi Arabia.
Iran has reported the most deaths from the coronavirus outside China, where the flu-like disease originated. Other Gulf Arab states have diagnosed the infection in several people who had visited Iran.
The official Saudi Press Agency, citing the Health Ministry, said people who had interacted with the infected man had been isolated and were being tested.
Saudi Arabia had since last week taken several measures to prevent the spread of the disease to the kingdom.
It imposed a ban on foreigners arriving for the Muslim umrah pilgrimage, Gulf Arab citizens visiting Mecca and Medina, home to Islam's two holiest sites, and tourists from at least 25 states where the virus has been found.
The Health Ministry said on Sunday it had prepared 25 hospitals to handle any coronavirus infections, with 2,200 beds dedicated for quarantine cases.
Pilgrimage is big business for Saudi Arabia, the birthplace of Islam, and is the backbone of plans to expand visitor numbers under an ambitious economic reform agenda.
The minor umrah pilgrimage, which can take place at any time of the year, brought 7.5 million people to Saudi Arabia in 2019, according to official figures.Visits by pilgrims accelerate during the fasting month of Ramadan, beginning this year in late April. And in late July, some 2 million pilgrims are expected for the week-long haj, the world's largest annual gathering of Muslims, which has a separate visa regime.