The 71-year-old arrived in Thailand on Friday with a fever which doctors in Oman could not treat, the ministry statement said.
"He tested positive for the MERS virus," and was quarantined in a Bangkok hospital, the statement said, adding "He is tired but conscious".
But authorities are looking for more than 250 people who may have come into contact with the man.
Of those, 37 were at "high risk" of contracting the virus, the ministry said, without giving further details.
It is the second recorded case of the virus in a kingdom which is visited by millions of people each year and is a hub for medical tourism.
The first case was also of an elderly Omani man, who was admitted to hospital in June last year but discharged weeks later after he was treated and declared virus-free.
The MERS virus first appeared in 2012 in Saudi Arabia.
South Korea was hit hard by an outbreak in 2015 which killed 36 people and caused panic across Asia's fourth-largest economy.
The virus is considered a deadlier but less infectious cousin of Severe Acute Respiratory Syndrome (SARS), which killed hundreds of people when it appeared in Asia in 2003.
