Scores of people have reported to the emergency services at hospitals in the city of Al-Ahsa in Eastern Province, after showing even the slightest signs of a fever.
"I felt the symptoms of a cold, accompanied by a fever," a young man told AFP by telephone from one hospital where he was admitted and placed in quarantine.
"I came to hospital. The symptoms disappeared by the end of the day, but I am still kept in a quarantine with other patients, which scares me," he said, asking to remain anonymous.
Fifteen of the 24 people who have contracted the coronavirus in Saudi Arabia since August have died, the kingdom's health minister Abdullah al-Rabia said on Sunday.
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A total of 13 cases have been detected in the King Fahd hospital, in Al-Ahsa. Among those was a nine-year-old girl who died a few hours after arriving at hospital with a strong fever.
Another fatality was Haidar Ghanem, a disabled 21-year-old man who had a "strong fever" for a week, according to his father Mokhtar. He died last Thursday, four days after being admitted to hospital after falling unconscious.
In all, 34 cases have been reported worldwide since the virus was first detected in September 2012, with 18 of the victims dying, according to the World Heath Organisation.
While the virus has been deadliest in Saudi Arabia, cases have also been reported in Jordan, Germany, Britain and France where two patients are now in hospital in the northern city of Lille.
The virus is a cousin of Severe Acute Respiratory Syndrome (SARS), which triggered a scare 10 years ago when it erupted in east Asia, leaping to humans from animal hosts and eventually killing some 800 people.