She alleged the minister threatened her with dire consequences if she told anyone about the incident.
The complainant recorded her statement before metropolitan magistrate Pradeep Modi on September 13.
On the magistrate's directions, the Sodala Police Station booked the minister on Tuesday. Nagar has also been charged with causing hurt to the woman.
Denying the allegations, Nagar termed the case a conspiracy against him. Earlier, Nagar has been accused of giving life threat to a BJP leader.