Carla Heatley was last seen at a flat in Hutchison Road around 12.45pm on Sunday 12 February.
Carla is described as white, around 5ft 6ins tall, of average build, with light-brown to blonde hair and has an Irish accent.
She was last seen wearing a navy Superdry parka jacket and black Nike trainers.
Carla has links to the Sighthill area and may have intended to travel there.
Inspector Neill Whiteside of Drylaw said: “We are concerned for Carla’s welfare and are asking anyone who may have seen her since this time to get in touch.
“If Carla reads this appeal, I would urge to get in contact with either us or her family as soon as possible.”
Anyone with information can contact Police Scotland on 101.