The woman, who is in her 60s, was walking alone at around 10.45 when the medium-sized brown dog jumped up at her, causing her to fall on to the concrete path.
She is currently being treated for a fractured skull in hospital and her condition is described as serious.
Police would like to speak with the three people who were with the dog at the time of the incident.
They are also urging any witnesses to come forward as a matter of urgency.