Jennifer Scott was transferred by helicopter from Dumfries and Galloway Royal Infirmary last week after she was diagnosed with a serious flu-type illness.
Ms Scott is being treated at the Glenfield Hospital in Leicester where there is specialist equipment to deal with such serious conditions.
It has been reported that 27 year-old Ms Scott, from Sanquhar in Dumfriesshire, was pregnant and collapsed at her mother's funeral.
At hospital, doctors performed an emergency caesarean section before Ms Scott was airlifted to Leicester.
A spokesman for NHS Dumfries and Galloway said: "We have had a confirmed case of a significant flu-type illness. That case has been transferred and there are no other confirmed cases."
A spokeswoman for University Hospitals of Leicester NHS Trust said; "We can confirm the patient has been transferred to Glenfield Hospital and is on an ECMO machine in intensive care."
The extracorporeal membrane oxygenation machine works in place of the heart and lungs.
The spokeswoman added: "The patient was flown to Glenfield Hospital as it is one of a limited number of hospitals in the UK that has this specialist piece of equipment. The patient is currently in a critical but stable condition."
Fears of a swine flu pandemic began in April 2009 after scores of deaths were reported in Mexico.
However, the problem became localised when two Scottish holidaymakers returned from Mexico and were confirmed as having swine flu. The holiday-makers were held in isolation at Monklands hospital in Airdrie.
By September 2009, however, Health Protection Scotland estimated the total number of people in Scotland who have contracted the H1N1 virus was 6181. The death total was nine.
The winter of 2009-2010 saw swine flu figures soar and scientists have since estimated up to two million people in Scotland may have been infected, according to research by Edinburgh University.