Authorities are trying to trace all 71 passengers on a Heathrow to Glasgow flight who may have been exposed to Ebola.
A woman returning home from Sierra Leone has become the first person in Britain to be diagnosed with the disease.
Britain's screening system for the disease immediately came under scrutiny after the NHS nurse's condition was not detected in either country.
Nicola Sturgeon, Scotland's First Minister, confirmed that a woman was being treated at Gartnavel Hospital in Glasgow after returning to Scotland via London.
She appealed for the public not to panic and said the chances of a wider outbreak were "negligible".
Scottish health authorities, Public Health England and British Airways were trying to trace all 71 passengers on the Heathrow to Glasgow flight who may have been exposed to the disease.
Sturgeon said that the woman, a voluntary aid worker seconded from NHS Scotland, had been screened for Ebola before she left the West African country on a flight operated by a Moroccan-based airliner that travelled via Casablanca.
She left Sierra Leone on December 28 and had been a passenger on flight AT596 from Freetown to Casablanca before catching flight AT0800 from Casablanca to London.
The woman was also tested on her arrival at Heathrow before she took a connecting flight - about four hours later - to Glasgow on Monday NZT, arriving in Scotland on Flight BA1478.
She started feeling unwell on Monday and was taken to hospital by ambulance, where she was placed into an isolation unit. Doctors said she was in a stable condition and her prognosis was good.
Save the Children confirmed the woman had been working in Kerry Town, Sierra Leone, and was an NHS Scotland employee.
The patient will be transferred to an isolation unit at the Royal Free Hospital, London, as soon as possible.
Sturgeon said the woman was screened twice but had displayed no symptoms of the disease. She said the risk of it passing to other passengers on the same plane was extremely low as it appeared to have been caught at a very early stage.
Experts said the disease could incubate for eight or nine days within a carrier but it could not be passed on until they start displaying serious symptoms such as vomiting, not merely a fever.