The incident happened shortly after 3pm on Saturday, on a footpath leading between Fauldburn and North Bughtlin Brae.
The 33-year-old female dog walker was heading south along the footpath when, just after a divide which leads to Drum Brae, a teenager exposed himself to her.
She continued to walk in the direction of North Bughtlin Brae as he shouted after her.
The suspect is described as white, 14-18, 5ft 7in with a medium build. He had black hair, which was short at the back and sides. The longer hair at the top was brushed forwards. He was wearing a plain black zip-up hoodie and blue jeans. On North Bughtlin Brae the dog walker met another woman who had just seen the suspect heading towards Fauldburn.
Detective Constable Bruce Raimondo of Edinburgh’s Public Protection Unit said: “We’re appealing for anyone who may have seen the suspect in the area around this time, or who recognises his description, to come forward.”