Middle East Respiratory Syndrome has killed over 300 people in Saudi Arabia since it first emerged there in 2012.
Coronaviruses cause respiratory infections in humans and animals. Symptoms are fever, coughing and breathing difficulties. It causes pneumonia and, sometimes, kidney failure.
The woman is said to be in a critical condition. “But she is responding well to treatment and is on the path to stabilization," a spokeswoman for the Vienna Hospital Association said.
Anybody she had been in contact with would be informed and checked for symptoms, a health ministry official told ORF radio.
The woman had gone to a doctor with ‘flu like symptoms, and the doctor immediately sent her to hospital. She is being treated in an isolation ward in a hospital which specializes in infectious diseases.
Mers coronavirus has a strong link to camels, but it is unclear how the virus passes from the animals to humans, and whether camels are the main source of the disease.