Joyce Kirkland was last seen around 10pm on Friday, March 12 within a house on Buchanan Street, Kirkcudbright.
She was reported missing at 4.50am on Saturday, March 13.
Joyce is described as around 5ft 6in, of medium build with grey shoulder length hair. It is unknown what she is wearing.
Sergeant Frank Parker, based at Castle Douglas, said: "We are concerned for Joyce's welfare.
"She has limited mobility issues due to problems with her knees so this may be noticeable as she would have to take regular rests when walking.
"Her family are extremely concerned, she has not been reported missing before and we are appealing for anyone who has seen Joyce to contact us."
Anyone with information should contact Police Scotland on 101 quoting incident number 0645 of March 13, 2021.