The patient, who contracted the virus in China, turned up at Lewisham hospital's A&E department in south London on Sunday and spoke to staff at the reception desk.
Public Health England (PHE) has been advising anyone who thinks they may have symptoms of coronavirus to stay at home and call NHS 111, who will send out a specialist team if needs be.
Two staff from Lewisham hospital are now in isolation at home after coming into contact with the woman, believed to be a Chinese national.
In a statement to the PA news agency, Ben Travis, chief executive of Lewisham and Greenwich NHS Trust, said: "There has been a confirmed case of coronavirus from a patient who self-presented at the A&E department of University Hospital Lewisham on Sunday February 9.
"The test result was confirmed as positive on Wednesday February 12 and we have been in touch with all staff who came into contact with the patient. The patient went to St Thomas' yesterday evening.
"Our colleagues in our emergency departments are following the latest advice and protocols from Public Health England. In this case, the patient self-presented at our A&E.
"As soon as the patient did this, the patient was given a mask and then escorted to be tested in the dedicated area we have assigned for coronavirus testing outside the A&E building - while awaiting the installation of a purpose-built 'pod'.
"In line with our protocols, throughout their care, the patient was escorted and did not come into contact with other patients.
"The patient was later discharged and taken home by London Ambulance Service.
"All staff who had direct contact with the patient have been contacted, including two members of staff who are undergoing active surveillance at home for a 14-day period as a precautionary measure - following the advice of Public Health England."
The woman remained at home while further checks were carried out.
Earlier this month, hospitals were told to create "priority assessment pods" for people with suspected coronavirus to keep them away from other patients.
The letter, from Professor Keith Willett, NHS strategic incident director for coronavirus, said plans were needed to avoid a "surge in emergency departments".
Patients who think they have symptoms will be directed to a pod away from A&E, from where they can call specialist NHS 111 teams on a dedicated phone, the letter said.
An assessment will be made by NHS 111 and staff told of the patient's location if further testing is deemed necessary.