Tests revealed the 38-year-old, who flew into the city on a connecting flight from Dubai on Tuesday, has Crimean-Congo haemorrhagic fever (CCHF).
He is said to be in a critical condition and is being treated in isolation at Gartnavel General Hospital's Brownlee Centre, which specialises in infectious diseases.
Three passengers who were sitting close to him on the Emirates flight EK027 from Dubai have been contacted by health officials to ensure there has been no transmission of the disease.
CCHF is a widespread tick-borne viral disease that is especially common in East and West Africa and is fatal in up to 30% of human cases.
The onset is said to be sudden, with initial symptoms including headache, high fever, vomiting and back, joint and stomach pain.
As the illness progresses, large areas of severe bruising, nosebleeds and uncontrolled bleeding at injection sites can be seen, beginning on about the fourth day of illness and lasting for about two weeks.
Outbreaks can usually be traced to a person having had contact with blood or body fluids from infected animals or people.
The man was admitted to hospital within three hours of his arrival in Glasgow and NHS Greater Glasgow and Clyde officials said all appropriate infection control measures were in place.
NHSGGC said the risk of the disease being passed from person-to-person is "extremely low" as it is not passed through the air.
In a statement, the health board said: "This man went into the care of the NHS within three hours of his flight arrival in Glasgow and travelled directly home via private transport from the airport, so we are confident his close contacts subsequently within the city were minimal.
"The risk to all other passengers on the flight is extremely low. However, if they have any concerns they should call NHS24 on 08000 858531 for advice, further information and reassurance.
"We have also identified all NHS staff, airport and airline staff who have had contact with the patient and any necessary follow-up action will be taken."
Dr Syed Ahmed, NHSGGC consultant in public health, is co-ordinating an investigation into the case, along with colleagues from Health Protection Scotland and the Health Protection Agency.
He said: "As soon as laboratory sampling confirmed the patient was suffering from this virus, all the appropriate agencies were informed."