Police have registered a case against him and three others for allegedly gang-raping a woman and molesting her daughter, a minor, in 2014.
Mr Prajapati has denied all the allegations.
A court sent him judicial custody for two weeks to allow police to question him.
The allegations were made against him 2014, but police registered a case only last month after protests from opposition parties and activists.
The former minister lost his seat in the recently concluded state assembly elections. His Samajwadi Party also suffered a crushing defeat at the hands of Prime Minister Narendra Modi’s Bharatiya Janata Party.
Scrutiny of sexual violence in India has grown since the 2012 gang rape and murder of a student on a Delhi bus.
However, brutal sexual attacks against women and children continue to be reported across the country.