Police said the man told the girl that he wanted to hire her as a model, after he contacted her on Instagram.
They said he claimed to worked at Base Models - a legitimate company, of which he was not an employee.
Base Models said anyone approached online by someone who claimed to work for them should contact their office.
In a statement posted on Facebook, police said that on Monday a 15-year-old girl from Cumbernauld, North Lanarkshire, was approached by a man on Instagram who asked her to expose herself to him on Skype.
Police also said the man asked the girl inappropriate sexual questions.
A statement from Base Models warned: "Be aware there are many individuals, fake photographers and scouts using the internet claiming to be affiliated or members of Base Models.
"Should you be contacted by anyone claiming to be any of the above, you should first contact our office immediately so we can verify their identity.
"Base Models never conducts interviews via Skype, never requests nude or lingerie photos and never requires any money from applicants."
Police Scotland said: "If you have been the victim of indecent communication by anyone online please contact us via 101 or attend at your local office to report the matter and seek advice."
Police have issued a warning after a man who posed as a scout for a model agency asked a teenage girl to expose herself to him on Skype.