Justin Bieber performs during New Year's Eve celebrations at Times Square in New York. REUTERS/Eduardo Munoz
The Sydney girl sent a friend request on an internet video-chat program last Monday to a person using a profile that included Bieber's photograph and personal details.
In subsequent online video conversations, the girl was asked to model revealing clothing.
The girl told her mother, who reported the matter to police.
"This incident serves as an important reminder that online predators will stop at nothing to groom children," State Crime Command's Sex Crimes Squad commander Detective Superintendent John Kerlatec said.
"We advise parents to educate their children about these dangers, and to warn them to be wary of anyone who claims to be famous."
Investigations are continuing.
