The owner of a vintage shop in London has alleged that Peaches ran out of the shop with the dress, and that she made no attempt to hide what she was doing.
According to The Sun, the owner has contacted police and Peaches is expected to be interviewed shortly.
A source told the newspaper: 'The assistant says she recognised Peaches as she came in.
'She says she saw Peaches rip the dress from a hanger and run out of the shop with it. It was apparently very blatant.
'The assistant ran after her, but didn't want to leave the shop unattended.
'There have been a number of misunderstandings over Peaches leaving shops without paying.
'The shop owner feels that, just because she is the daughter of a rock star, it doesn't mean she shouldn't have to face the law like everybody else.'
Police confirmed they were investigating the alleged theft but Peaches' spokesman said: 'Peaches knows nothing about any allegation of shoplifting and has not been contacted by police.'