The couple, believed to be tourists, told police they were approached by a "lewd" man in the early hours of this morning.
Officers are investigating the claims of the couple, who put up their tent in the shadow of the National Monument last night.
They said that in the early hours of this morning a man approached their tent, and then made "lewd" and inappropriate advances towards them.
Investigators cordoned off a small area of the popular tourist spot this morning to photograph the site.
A police spokesman said: "We are looking into a report that a man made a lewd approach to a couple of campers on Calton Hill in the early hours of this morning."
While it is one of the most popular tourist attractions during the day, Calton Hill has a less savoury reputation at night, when it has been a regular haunt of male prostitutes.
Camping on the hill is not illegal, although a member of staff at outdoor equipment store Black's said it was not something that they would recommend.
City centre councillor David Beckett said an incident such as this would be of concern to local residents. "There have been a lot of problems there in the past, and local residents would be concerned to hear about something like this," he said.
"I'm not aware of a lot of people camping on Calton Hill, perhaps because the area does have something of a reputation, but if these people have camped there and have been exposed to that then it is very unfortunate.
"We will work with the police, and with the local community officer, to make sure we can give them any assistance they need, and I would also like to see more patrols around Calton Hill, to further reduce the likelihood of crime being committed there."
Concerns were raised recently that sex workers who have traditionally plied their trade on the north of the hill had been seen working near homes in the area.
It was thought that a rise in the number of drug addicts, teenage drinkers and homeless people using the hill in the evenings had disturbed the sex workers and forced them to move elsewhere.
Despite being linked with such activities, the hill, home to the David Hume Mausoleum, the Dugald Stewart Monument and Nelson's Monument, is still one of the most popular tourist attractions in Edinburgh.