Peaches Geldof has apologised for tweeting the names of the two mothers who let their babies be abused by Lostprophets singer Ian Watkins.
Geldof, daughter of Boomtown Rats singer Sir Bob Geldof, tweeted the names to her 160,000 followers after believing they were in the "public domain".
The TV presenter and model later deleted the tweets. Police confirmed they will be investigating the incident.
Victims of sexual abuse are guaranteed anonymity by law for life. The names of the two women who went on trial with the disgraced Lostprophets singer were never released in order to protect the identities of their children.
In a series of tweets apologising for identifying the two women, she said:
"I deleted my tweets and apologise for any offence caused as at the time of tweeting [I] had only seen everyone tweeting the names at me so had assumed as they were also up on news websites and the crown courts public file that they had been released for public knowledge.
"Will check my facts before tweeting next time. Apologies and lesson learned."
She added: "The question of whether or not to give anonymity to criminals in cases like this will go on forever. However these women and Watkins will be getting three meals a day, a double bed, cable TV etc- all funded by the tax payer alongside not being named apparently. It makes me sad."
Det insp Peter Doyle, of South Wales Police, said the force is aware of the controversy surrounding Geldof's tweets and will be investigating the incident.
"Clearly, there is strong public feeling about this case and many people are using social media forums to talk about the issues involved.
"We are currently in consultation with the Crown Prosecution Service regarding the matter and will take action if appropriate."
Police previously warned people against discussing the Watkins case on social media in case they reveal the names of the victims or Watkins' two female accomplices.
Doyle added: "There is a very real danger that some of the detail being posted will lead to the identification of victims which will cause a great deal of distress to them and their families."
In 2012, nine people were fined £624 each after they revealed the name of the woman who was raped by former Sheffield United footballer Ched Evans.
James Baines was recently handed a 14-month suspended jail sentence and ordered to pay £3,000 in costs after he tweeted images of a person he claimed was James Bulger's killer Jon Venables as an adult.
Watkins pleaded guilty to 11 sex offences at Cardiff Crown Court, including attempting to rape a baby.
He was described as "a determined and committed paedophile" who exploited his celebrity status in order to abuse young children.