They said concern was growing for the welfare of Louise Davidson who was last seen at about 04:30 on Tuesday outside the Espionage nightclub.
She was thought to be heading from Victoria Street towards the Underbelly venue in the Cowgate.
Louise, who is from Kirkcaldy in Fife, is 5ft 5in tall with long black hair.
She was wearing jeans and a black crop-top.
Sgt Neil McGurk said: "It is unlike Louise not to get in contact with friends or family and let them know where she is and as such we are eager to establish her whereabouts as soon as possible.
"Anyone who believes they have seen her since the early hours of Tuesday morning is asked to contact police immediately.
"We would also urge Louise to get in touch with a family member, friend, or with police to let us know she is safe."
Police are trying to trace a 19-year-old woman who has not been seen since leaving an Edinburgh nightclub, possibly in the company of two men.