Watkins, the former front man for the band Lostprophets, this week pleaded guilty in a Welsh court to numerous child sex-abuse charges, including the attempted rape of a baby. He also confessed to conspiring with two groupies to sexually assault their children.
The women's names have not been released to the public in the United Kingdom, however, Peaches Geldof mentioned them when she voiced her outrage over the case online, the BBC said.
She later deleted the tweets and apologized, explaining she read the names of the women on a U.S. media website and assumed they were already "public knowledge."
"Will check my facts before tweeting next time. Apologies and lesson learned," she said in a Twitter message Thursday.
The South Wales Police told the British broadcaster it is discussing the tweeting issue with the Crown Prosecution Service.