Edis Kayalar, 26, who has been charged with attempting to extort $100,000 (€67,000 euros) from Crawford by threatening to publish the photo, handed himself into police late Monday evening, a spokesman told AFP.
Kayalar, already known to the police for drug-related offences, was being questioned, the spokesman said.
The photo was apparently taken by the couple's former nanny and shows the girl, then aged seven and now eight, tied to a chair wearing shorts and a T-shirt, according to court papers.
The girl told her parents, who were unaware of the image, that the nanny had taken the photograph as part of a "cops and robbers" game, according to an affidavit filed in the case.
Kayalar, a friend of the nanny, took possession of the photo and threatened Crawford, 43, and her husband Rande Gerber with its release unless they met his demands, officials said.
The couple reported the extortion attempt as soon as Kayalar approached them, authorities said, triggering an FBI investigation.
Kayalar, a professional model according to entertainment site TMZ.com, has been charged with one count of extortion, which carries a maximum sentence of two years.