Siobhan McLeod, or who sometimes goes by the surname Sinclair, was last seen outside an address in Den Park, Abernethy at about 4.30pm on Thursday, 18 March.
The 31-year-old is white and has long black hair which she usually has up in a clip.
At the time she went missing, Siobhan is believed to have been wearing black silky trousers, a white top with black writing and a black puffy jacket.
There are increasing concerns for her welfare and officers understand she may have travelled to the Perth area.
Sergeant Lesley McDonald of Perth Police Station said: “Along with her friends and family, we are becoming increasingly concerned for Siobhan’s welfare and are keen to locate her as soon as possible.
“I would urge anyone who may have seen Siobhan to contact us immediately. Similarly, if Siobhan is reading this, let us know you are safe and well.”
Anyone with information is asked to contact Police Scotland on 101, quoting incident 2650 of 18 March.