Ramadan was summoned for questioning to a Paris police station and taken into custody "as part of a preliminary inquiry in Paris into rape and assault allegations", legal sources told news agencies, confirming a report by RTL radio.
Last October Henda Ayari, a former Salafist who has become a secular feminist, accused Ramadan of raping her.
Her allegation came as the fallout from the #Metoo movement, inspired by the scandal over Hollywood film moghul Harvey Weinstein, hit France.
A week later another woman filed more charges, reportedly supplying doctors' certificates to back up her account of an assault in a hotel in a provincial French city.
Ramadan denied Ayari's accusations and sued her for libel.
Some of his supporters launched a social media campaign against her.
Ramadan, who is the grandson of the founder of Egypt's Muslim Brothers, is a controversial figure in France, where he has had some support among Muslims and been accused of trying to smuggle Islam into politics by his detractors.
The rape allegations sparked a row between the vehemently secular Charlie Hebdo paper and the Mediapart website over the left's attitude to Islamism.