Emergency services were called to an incident in the town's Winterhope Road on 3 December.
Yvonne Elaine Fitzner, 48, was found inside the building and taken to Dumfries Infirmary for treatment.
Police said she died in hospital on Monday. They added there were no suspicious circumstances.
The procurator fiscal has been informed.
Police have confirmed that an Annan woman has died in hospital 11 days after being rescued from a house fire in the town.