The woman, who was at Dungavel Detention Centre, in Lanarkshire, was taken to hospital on Thursday for tests.
She is believed to be in her 30s and arrived recently from Sierra Leone, where hundreds have been killed by the deadly virus.
The woman, who was initially held at a UK airport, has been taken to the infectious diseases unit at Monklands General Hospital.
A spokesman for NHS Lanarkshire confirmed one person is being investigated as precaution and said it was "highly unlikely" they would test positive for Ebola.
He added: "We are currently investigating a possible case of Viral Haemorrhagic Fever (Ebola).
"This is a precautionary measure and it would appear at this stage to be highly unlikely the patient will test positive for Ebola."