Lawyers for her father claimed the social media giant's open registration system allows children to log-in and could put them at risk from paedophiles.
It was alleged that the current arrangements are not fit for purpose.Under Facebook's policy no-one under 13 is allowed to use the site.
But the girl, who is subject to a care order, has reportedly posted suggestive images of herself on it since she was 12.
She has used up to four different accounts on the site and been in exchanges with a man who is restrained from any contact with her, the court heard.
Legal proceedings were launched in a bid to secure an injunction compelling Facebook to take steps to prevent the girl using the site or publishing images on it.
In court, on Wednesday, barrister Peter Girvan claimed there has been a breach of her privacy.
He contended that her highly sexualised contact with men on the site was degrading, abusive and harassing.
According to Mr Girvan, the open registration system was flawed because 13-year-olds cannot enter a contract or legally consent to their data being used.
Even younger children could claim to be the required age and give themselves a fake name, it was argued.
It was further argued that Facebook could change its terms of registration to require users to verify their identity and age.
The case could have potentially significant implications for the social networking company's operation in the UK.
It was pointed out that if a ruling is made in favour of the girl's family it may prevent huge numbers of child users from accessing the site.
Mr Justice McCloskey is due to deliver his verdict in the injunction application later this week.