The girl was touched inappropriately by a man while with her mother at Portobello beach, Edinburgh, at around 2.15pm on Saturday, police said. The man is described as white, in his mid-to-late thirties and around 6ft with dark hair and glasses. He was wearing a pink or orange t-shirt, dark blue shorts, white trainers and had a black bumbag around his waist.
Police Scotland's Detective Inspector Dougie Moran said: "We are still trying to establish exactly what has happened during this incident and have been following up a number of lines of investigation since the matter was reported to us."
Anyone with information is asked to call police on 101.