Sarah Fletcher, from Partick, was last seen by relatives at around 8.40am yesterday, when she left her home in Dumbarton Road.
Police said her family are "extremely concerned" about her.
She is described as white, around 5ft tall, with brown hair, and glasses.
When last seen, she was wearing a green top with a tan jacket, brown leggings and brown or grey boots.
Police believe she may have travelled to Stirling around lunchtime yesterday. She also has connections in Dundee and St Andrews.
Inspector Matthew Webb said: "It's out of character for Sarah not to have been in touch with her family or friends and she has never gone missing before.
"We just want to know she is safe and well. Her family are very worried."
Anyone with information is asked to contact Partick Police Office on 101.