The Saudi health ministry had informed the UN's health body that the patient had been hospitalized on January 29 and had died on February 10, WHO said in a statement.
A laboratory had confirmed on February 18 that the person had died from the so-called novel coronavirus, or NCoV, it added.
This brings to 13 the number of cases of the virus that have so far been reported to the WHO since it was first detected in the middle of last year, with six previous fatalities -- three in Saudi Arabia, two in Jordan and one in Britain.
The news comes just days after a person suffering from the virus died in hospital in central England on Sunday.
That patient, who had a pre-existing health condition, was one of three people in the same family with the virus, which appeared to have been caught by one of the family members during a recent visit to the Middle East and Pakistan.
Even before the death in Britain, the WHO had on Saturday urged its member states to keep a close eye on any cases of severe acute respiratory infections, like pneumonia, and to "carefully review any unusual patterns."
Health authorities should test for NCoV in cases of unexplained pneumonia or other severe, "progressive or complicated respiratory illnesses not responding to treatment, particularly in persons traveling from or resident in areas of the world known to be affected," it said.
It also urged testing of any health workers showing such symptoms, and thorough investigations of clusters of cases, regardless of where they occur in the world.
WHO meanwhile did not recommend any travel or trade restriction in connection with the virus.
Coronaviruses cause most common colds but can also cause SARS (severe acute respiratory syndrome).
The new virus however is different from SARS, especially in that it causes rapid kidney failure.
A SARS epidemic killed more than 800 people when it swept out of China in 2003, sparking a major international health scare.