The elderly lady was walking near to the Midsteeple when she was approached and then attacked by a man who took hold of her, knocking her to the ground.
The man then took hold of her bag before he made off from the scene at around 4 am.
Police were alerted and the woman was taken to Dumfries and Galloway Royal Infirmary were she was treated for a head injury.
Appealing for witnesses, Detective Sergeant Graeme Roberston said: “This is a very unusual type of attack to have happened in Dumfries and whilst we know that the streets would have been quiet at this time, we are appealing to the likes of delivery drivers or people going to work to get in touch if they were about the area, saw this man or can help in any way.
“We are reviewing CCTV images from the town centre cameras at this time. The man we want to trace is described as approximately 5 – 5’ft in height wearing dark trousers and white trainers.”
He added: “Enquiries are in their infancy and further details may be furnished at a later time.
“Fortunately the woman in this attack was not seriously injured and is recovering from what must have been a horrific ordeal for her.”
Anyone who can help should call police on the 101 number, quoting the reference number 0421 25/6. Callers who wish to remain anonymous can call Crimestoppers on the 0800 555 111 number.