"We have received more than 300 insulting emails of which several contain death threats," Closer said, adding that it had notified the police.
Fourteen of the most violent messages addressed to Pieau were handed over to the police. One vowed to "never let her stay in peace."
After their debut in the French weekly, the photos of the British Duchess of Cambridge have appeared in magazines in Denmark and Sweden, Ireland's Daily Star and Italy's Chi, which like Closer is owned by former prime minister Silvio Berlusconi's Mondari media group.
The pictures were taken when the royals were vacationing in southern France at a chateau owned by Viscount Linley, the son of Princess Margaret, the deceased sister of Britain's Queen Elizabeth II.
After publication, Pieau defended them saying they were not in the "least shocking".
"They show a young woman sunbathing topless, like the millions of women you see on beaches," she told AFP.
The royal family's lawyers have obtained a civil injunction and sought criminal charges in Paris, including against the unidentified photographer, in a bid to curb the spread of the pictures.
French legal authorities have banned Closer from any further distribution of the pictures and began a criminal probe into how they were obtained.
The court also ordered the magazine to hand over the files with the images to the royal couple, which the publication has done.
Closer has said it does not own the images and simply bought them for exclusive first use, so it likely does not possess all the original files. It has refused to say from whom it bought them or who is the photographer.
The French court also banned Closer from reselling the pictures or reusing them in print or on its website.