Emilie Anderson was last seen by friends at about 02.30am in Market Street in Galashiels.
No sightings of the 26-year-old have been reported since then, prompting concerns for her welfare.
Inspector Bryan Burns, of Melrose police station, said: " Around 2.30am on Sunday, March 1, Emilie was last seen walking in Market Street in Galashiels, and we are growing increasingly concerned for her welfare of her.
"I am appealing for any persons who may know of her whereabouts or anyone that may have seen a female walking in that area of Galashiels to contact police urgently.
"Inquiries are ongoing, and we are working with partners to trace her."
Emilie is described as white, 5ft 2in tall and of slim build, with brown hair.
When last seen, she was wearing dark jeans, a dark-coloured bomber-style jacket and flat white shoes.
Anyone with information on her whereabouts is asked to call Galashiels police station on 101, quoting reference number 3,672 of March 1.