While she was trying to call the police a runner and another cyclist stopped to say they too had been threatened by the man.
It is the latest in a series of similar incidents on the Craiglockhart/Meggetland section of the 31 mile (51km) canal.
Insp Keith Forrester, of Police Scotland, confirmed the incident involving the nine-year-old. He said they were aware of other reports of similar behaviour in the area, but that they were not linked.
He said inquiries were ongoing and that they were reviewing CCTV from the area.
“We are aware of concerns in the community following reports recently of assaults and threatening behaviour on footpaths along the Union Canal in the Edinburgh area,” he said.
“Community policing teams are carrying out additional, high visibility patrols of the area.”
