The woman, who arrived from Sierra Leone on Sunday night, is in isolation at Glasgow’s Gartnavel Hospital.
All possible contacts with the case are being investigated, including on flights to Scotland via Heathrow.
The woman will be transferred to specialist high level isolation in London as soon as possible.
At a news conference in Glasgow, First Minister Nicola Sturgeon stressed that the risk to the general public was very low.
She added that the patient was thought to have had contact with only one other person since arriving in the city, but that all passengers on the flights the woman took will be traced.
Alisdair MacConachie, of NHS Greater Glasgow and Clyde, said the woman was “not showing any great clinical concern”.
NHS Scotland said infectious diseases procedures had been put into effect at the Brownlee Unit for Infectious Diseases at Gartnavel, reports the BBC.
The patient returned to Scotland from Sierra Leone late on Sunday via Casablanca and London Heathrow, arriving into Glasgow Airport on a British Airways flight at about 23:30.
While public health experts have emphasised that the risks are negligible, a telephone helpline has been set up for anyone who was on the Heathrow to Glasgow flight. The number is: 08000 858531
The patient was admitted to hospital early in the morning after feeling unwell and was placed into isolation at 07.50.
A British Airways spokesman said: “We are working closely with the health authorities in England and Scotland and will offer assistance with any information they require.
“The safety and security of our customers and crew is always our top priority and the risk to people on board that individual flight is extremely low.”
Ms Sturgeon has chaired a meeting of the Scottish Government Resilience Committee (SGoRR) and has also spoken to Prime Minister David Cameron.
According to UK and Scottish protocol for anyone diagnosed with Ebola, the patient will be transferred to the high level isolation unit in the Royal Free hospital, London.
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