The mother, who gave birth at 5am on Tuesday, was cared for by a Red Cross team and both she and her baby are said to be in good health. They have been taken to hospital in Graz.
An interpreter was sent to the hospital on Tuesday and will speak to the woman about her plans and how long the doctors recommend she should stay in hospital. The majority of refugees arriving in Spielfeld are keen to travel on to Germany as soon as possible.
In recent days the number of refugees and migrants crossing the border has risen sharply.
On Tuesday morning around 3,800 refugees were waiting in Spielfeld for buses and trains. A further 3,600 people were waiting on the Slovenian border to cross into Austria.
Police expect more people to arrive later in the day, but have said that emergency accommodation is already full and that therefore people will have to wait in Spielfeld before they can be transported further.