Lucia Piacentini (44) was last seen by her partner at their home on Kirkwell Road on Sunday (July 28), around 6.45pm.
She is described as white, around 5ft4 and of stocky build, with short black hair and brown eyes.
Lucia was last seen wearing a burgundy hooded top and a khaki-coloured skirt. She may also have been carrying a red Berghaus rucksack.
According to investigating officers, the missing woman suffers from depression, and does not have her prescribed medication with her.
Inspector Taylor Grant, of Cathcart police office, said: “Ms Piacentini has not been missing before and it is completely out of character for her not to contact her family or friends.
“Despite extensive enquiries in the local area, we have been unable to trace Lucia. We have spoken with her family members, and, understanably, they are extremely concerned for her wellbeing and her safety.
“We have also liaised closely with our partner agencies, but there have been no sightings of Lucia.
“I would urge anyone with information regarding her whereabouts to contact Cathcart police office on 532 4900 or 101, the non-emergency number.”
Inspector Grant added: “I would also ask Lucia herself to give the police or her family members a call to let us know she is safe and well.”