"One of the patients who had contracted the virus has died," in the Eastern Region of Saudi Arabia where most of the kingdom's cases have been registered, the ministry said.
It did not identify the victim, but said he was a diabetic who also had heart and kidney problems.
The ministry also said that the health of a nurse who had been infected by patients in the Eastern Region was now improving.
"This is the first time health care workers have been diagnosed with nCoV (novel coronavirus) infection after exposure to patients," the WHO said in a statement.
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On Saturday, the health ministry said a new case had been detected, bringing to 31 the number of officially recorded cases in the country.
Since last September, the WHO says it has been informed of a global total of 40 laboratory confirmed cases of the virus, including 20 deaths.
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.