The 14-year-old was walking with a friend along Stenhouse Crescent at about 19:35 on Monday when they were approached from behind by a man.
He assaulted one of the girls before running back towards Stenhouse Gardens.
The man is possibly in his 30s, between 5ft 8ins and 5ft 10ins, of slim to medium build and was wearing all black clothing including shoes.
He was wearing trousers, a hooded top and a woollen hat.
Det Insp Kevin Harkins of Police Scotland said: "The girls were understandably distressed by this incident and immediately after they walked onto Calder Road where they spoke to a woman waiting at a bus stop with two young children aged about five and seven.
"We are yet to speak to this woman and so I'm appealing for her to come forward and speak to us.
"I also want to speak to anyone who may have seen the man in the area before or after the assault, he was on foot and may have been running along Stenhouse Crescent or the surrounding streets.
"This type of incident is unusual, and officers will be carrying out door to door inquiries as well as high visibility patrols.
"I would encourage anyone with information to speak to an officer or call police."
A teenage girl has been indecently assaulted by a stranger in an Edinburgh street.