Travellers coming from any fellow GCC state - the United Arab Emirates, Bahrain, Kuwait, Oman and Qatar - must spend 14 continuous days there and show no signs of the coronavirus before being granted entry, SPA said, citing an interior ministry source.
Saudi Arabia reported its first case of coronavirus on Monday in a Saudi national returning from Iran, which has reported the most deaths outside China, where the flu-like disease originated.
The other GCC states have also diagnosed the infection in people who had visited Iran, totalling more than 145 cases.
The Saudi health ministry said it was testing 70 people who had come into contact with the infected Saudi citizen, who remains in quarantine in hospital. The authorities have said he had not disclosed his visit to Iran upon returning home.
Iran hosts several important shrines and pilgrimage sites for Shi'ite Muslims, who make up a minority of Saudi Arabia's population.
The Saudi foreign ministry tweeted a video on Tuesday reminding citizens of an existing ban on travel to Iran, which is locked in a struggle with Saudi Arabia for regional supremacy.
Saudi Arabia took several measures last week to prevent the spread of the disease to the kingdom, banning foreigners arriving for the Muslim umrah pilgrimage, Gulf Arab citizens visiting Mecca and Medina, and tourists from at least 25 states where the virus has been found.
SPA also said that Saudi citizens or residents entering from a GCC country must inform authorities upon arrival in the kingdom of any travel outside the GCC in the preceding 14 days.
The kingdom will cooperate with any GCC country that wishes to apply the same procedures to travellers from the kingdom, it added.
Saudi Arabia's Center for Disease Control late on Monday urged citizens to postpone non-essential travel to Germany and France, where more cases have been reported.
