But the Geneva-based global health agency says it doesn't have enough information to estimate whether the new infection was the result of person-to-person spread.
The case is from Saudi Arabia, the ninth from that country.
Globally there have now been 16 confirmed infections from the new virus — which is from the same family as SARS — with at least nine deaths.
The WHO statement says the newest case was a contact of a 39-year-old Saudi man who died from the infection on March 2.
The newest case is a person who had mild illness only; the person has recovered and has been released from hospital.
The WHO says currently it doesn't know enough to gauge whether the new case was infected by the 39-year-old man, or contracted the virus from the same source as he did.
In fact, it appears that the WHO may know very little about the new case.
The press release from the agency does not reveal the individual's gender or age. Nor does it say when the person fell ill, was hospitalized and released from hospital.
WHO press releases announcing infections with the new coronavirus — which it calls NCoV — generally contain those kinds of details when the health agency has them.
If it turns out this is a case of person-to-person spread, it would not be the first time that has been seen.
There have been at least three instances where human-to-human spread is suspected, and in one of those cases it is assumed to have happened.
That instance involved a cluster of cases in Britain, started by a man who returned home ill after a trip to Pakistan and Saudi Arabia. The man's son, who had cancer, became infected and died. Another member of their extended family was infected, but she had only mild illness.
As the son and the third case in that cluster had not travelled outside Britain before becoming ill, it is believed they contracted the virus from the man who had travelled.
A British newspaper, the Birmingham Mail, reported Saturday that the first case in that cluster succumbed to his illness this week. But the WHO's statement Saturday does not reflect an additional death caused by the coronavirus.
The new virus was first spotted last June after a man from the Saudi capital, Riyadh, died from an infection for which a cause could not initially be discovered.
Subsequently it was recognized that earlier cases had occurred in Jordan, where 11 people fell ill last April in a cluster of mysterious infections in a hospital. Stored samples from the two fatal cases in that cluster later revealed they had been infected with the coronavirus.
When a blood test to determine past infection becomes available, it may be possible to determine if others in that cluster were also infected. But to date laboratories working to develop a blood test that picks up these cases has proved difficult to develop.
To date four countries have recorded infections: Saudi Arabia, with nine cases and six deaths; Qatar, with two cases; Britain, with three cases and one (or two) deaths; and Jordan, with two fatal cases.