Dozens of members of the ruling Saudi royal family, as many as 150, have been infected with coronavirus in recent weeks, a news report said.

Saudi Prince Faisal bin Bandar bin Abdulaziz Al Saud - the governor of the capital Riyadh who is in his 70s - is in intensive care after contracting the virus, according to The New York Times, which cited hospital communications, doctors in the country and sources familiar with the family.

King Salman and Crown Prince Mohammed bin Salman (MBS) have retreated into isolation to avoid the outbreak.

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Doctors at an elite hospital that treats royals are preparing 500 more beds for an expected influx of patients.

"Directives are to be ready for VIPs from around the country," the operators of the elite facility, the King Faisal Specialist Hospital, wrote in a "high alert" sent out electronically on Tuesday to senior doctors and later obtained by the Times.

"We don't know how many cases we will get but high alert," said the message, which instructed "all chronic patients to be moved out ASAP" and only "top urgent cases" will be accepted, according to the newspaper.

The alert added any infected staff members will now be treated at a less elite hospital to save room for royals.

There are thousands of Saudi princes. Many travel regularly to Europe and some are believed to have contracted the virus abroad and brought it back to Saudi Arabia, the report said.

The kingdom of about 33 million people has reported 2,932 cases and 41 deaths.

The country, home to Islam's holiest sites Mecca and Medina, banned the year-round Umrah pilgrimage and sealed off the areas in early March.

Travel in and out of the country, as well as between provinces, has since been largely restricted, and four governates and five major cities have been placed under 24-hour lockdown.

Authorities have yet to announce whether they will proceed with this year's Hajj, scheduled for the end of July. Last year, about 2.5 million people travelled to Saudi Arabia to take part in the Hajj, which all Muslims must perform at least once in their lives if able.

Worse to come

So far, mostly members of lower branches of the royal family have been infected, a source familiar with the situation told the Times. The vast majority of cases in the country have been in migrant labour camps and slums around Mecca and Medina.

But as the outbreak in the country spreads, Salman, the 84-year-old king, secluded himself on an island palace near Jeddah, while the crown prince has moved to a remote site on the Red Sea coast.

A Saudi health minister on Tuesday warned the outbreak in the country may only be beginning.

"Within the next few weeks, studies predict the number of infections will range from a minimum of 10,000 to a maximum of 200,000," Tawfiq al-Rabiah said, according to the official Saudi Press Agency.

The Saudi royal family is estimated to have about 15,000 members.

In early March, several royals and officials were arrested in what some observers said may have been a crackdown related to a plot to remove MBS.