The girl was touched inappropriately by a man while with her mother at Portobello beach, Edinburgh, on Saturday, police said.
Officers are appealing for witnesses to the incident, which happened at around 2.15pm.
Police Scotland's Detective Inspector Dougie Moran said: "We are still trying to establish exactly what has happened during this incident and had been following up a number of lines of investigation since the matter was reported to us.
"We are now keen to hear from other members of the public who were on the beach at the time.
"In the meantime, we have a high-visibility presence in and around Portobello beach to engage with the public, gather information and offer reassurance to the local community."
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 bum-bag around his waist.
Anyone with information is asked to contact police on 101.