The 53-year-old Food and Civil Supplies Minister sent his resignation to the Chief Minister's Office.
"I have resigned on moral grounds so that an impartial probe can be carried out as I am not guilty in the alleged case", Nagar told reporters at his residence.
"I sent my hand written resignation to the CMO through a person this morning. After many thoughts and second thoughts, I decided to resign...no one asked me to do this", he said.
When contacted, Press Advisor in CMO Mohd Yasin told PTI that the Chief Minister was in Barmer for a function and he had no information of Nagar's resignation.
The Sodala Police station had booked Nagar for allegedly raping, threatening and beating up the woman on September 11, after calling her to his official bungalow in Civil Lines on the pretext of giving her a job. After registering the case under various sections of the IPC including 376, police referred the case to CB-CID as it involved an MLA of the present Assembly.
The state's CID-Crime Branch had yesterday begun probing the charges of rape and assault levelled against Nagar. The woman's statement was recorded and her clothes, which she wore on the day of the alleged crime, were recovered and sent for forensic examination.
Chief Minister Ashok Gehlot had yesterday said that no one is above law and that law will take its own course.
"I told earlier also during the Asaram case that no one is above law," he had said.
Media frequently alleges that the government interferes in CBI investigation and that it influenced the recent Asaram case, but the state government never gets involved in any case, Gehlot said.