They took the death toll in Saudi Arabia to 157 since MERS, a coronavirus like Severe Acute Respiratory Syndrome (SARS), was identified two years ago.
The World Health Organisation said on Wednesday that while concern about the virus had "significantly increased", the disease was not yet a global health emergency.
Of the 16 new cases identified on Wednesday, two had died. Of the four cases identified on Tuesday, one had died, the ministry said.
SARS which killed around 800 people worldwide after emerging in China in 2002. It can cause coughing, fever and pneumonia, and there is no vaccine or anti-viral treatment against it.
The rate of infection in Saudi Arabia has surged in recent weeks after big outbreaks associated with hospitals in Jeddah and Riyadh. The total number of infections nearly doubled in April and has risen by a further 25 percent already in May.
The recent upsurge is of particular concern because of the influx of pilgrims from around the world expected in July during the Muslim fasting month of Ramadan.
Scientists around the world have been searching for the animal source, or reservoir, of MERS virus infections ever since the first human cases were confirmed in September 2012.