"An 81-year-old woman who was suffering from kidney failure as well as other chronic illnesses has died" in the eastern Al-Ahsaa region of oil-rich Saudi Arabia after contracting the virus, it said.
Saudi Arabia counts by far the most cases, with 30 confirmed infections and 18 fatalities, while cases have also been detected in Jordan, Qatar, Tunisia, the United Arab Emirates, Germany, Britain and France.
So far, there have been 44 lab-confirmed cases worldwide of the virus, which until now has been known as the novel coronavirus, or nCoV-EMC, but was this week redubbed the Middle East Respiratory Syndrome Coronavirus, or MERS.
In Saudi Arabia most cases have been registered in the kingdom's east, with the health ministry saying that most of those who died were "elderly people with chronic illnesses".
However, since May 18, no new cases have been registered in Al-Ahsaa while nine people who had been infected have now been cured, the ministry added.
The World Health Organisation said on Friday that much uncertainty remained surrounding MERS, stressing that it aimed to work closely with Saudi Arabia, Tunisia and perhaps other Middle Eastern countries to determine how great the risk is.
Saudi Arabia had announced it would send samples taken from animals possibly infected with a deadly SARS-like virus to the United States for testing in a bid to find the source of disease.
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.
Like SARS, the new virus appears to cause an infection deep in the lungs, with patients suffering from a temperature, cough and breathing difficulty, but it differs from SARS in that it also causes rapid kidney failure.