The woman arrived into Dublin Airport from Italy and then traveled to Northern Ireland
Dr John Cuddihy says those sitting within two rows of the woman have been given specific advice on self isolation
All other passengers have been notified and given more general advice.
The HSE says it will not be introducing any further measures, despite the confirmation of the first case on the island of Ireland.
The Health Minister is urging people not to spread rumours on social media over the coronavirus.
Simon Harris insists information needs to come from public health experts only: