The patient, who has contracted Crimean Congo Viral Haemorrhagic Fever, is in isolation in the Brownlee specialist unit at Gartnaval General Hospital.
NHS Greater Glasgow and Clyde Health Board say that although the risk he transmitted the fever to others was slim, it wants to trace anyone who may have been in contact with him.
The man, whose nationality has not been given, flew into Glasgow Airport aboard Emirates Flight EK027 at 12.35pm on Tuesday from Dubai. He was taken to hospital three hours later.
The board is already contacting three passengers who had been seated near him.
The fever, which is commonly found in the Middle East and Eastern Europe, can appear suddenly.
Symptoms including headache, high fever, back pain, joint pain, stomach pain and vomiting.
Sufferers may also have red eyes, a flushed face, a red throat, and red spots in the mouth.
Infection control staff have also identified all NHS employees, airport and airline staff who have had contact with the patient and say any necessary follow-up action will be taken.
Dr Syed Ahmed, NHS Greater Glasgow and Clyde consultant in public health said: "The risk of person-to-person transmission of Crimean Congo Viral Haemorrhagic Fever is extremely low as it can only be transmitted by direct contact with infected blood or body fluids.
"It is not a virus which is transmitted through the air. As such the risk to those who were in close contact with him is minimal.
"Crimean Congo Viral Haemorrhagic Fever is a widespread tick-borne viral disease.
"It is not common in Western Europe but is endemic in parts of eastern and southern Europe, central Asia, Africa, the Middle East and the Indian subcontinent.
"As soon as laboratory sampling confirmed that the patient was suffering from this virus all the appropriate agencies were informed."
The NHS24 helpline number for anyone on flight number EK027 to call if they have any concerns is 08000 85 85 31.