Dominique Strauss-Kahn, 62, was freed from house arrest last week after new information cast doubt on the woman's credibility.
She filed a libel lawsuit Tuesday against the tabloid. A series of Post articles over the weekend said the 32-year-old was a "prostitute," and a "hooker" and that she "traded sex for money."
The tabloid is standing by its reporting, according to a spokeswoman.
Meantime in Paris, a French novelist formally filed an attempted rape claim against Strauss-Kahn. The alleged incident happened in 2003.
Tristane Banon said she had waited eight years before filing her complaint because "it's very difficult for any woman in this situation ... and it's even more difficult when you know in advance that it's doomed to failure."
Banon said she described some of the attack in an "autobiographical novel" she published in 2006 called "The Trapeze Artist."
If Banon's complaint leads to preliminary charges, there will then be a lengthier investigation, sometimes lasting years, to determine if the case should go to trial before a judge.
The Associated Press contributed to this report.