Nagar, who resigned Thursday, claimed innocence and alleged that he was being framed in "a political conspiracy".
He told reporters that he sent in his resignation letter to Gehlot's office so that the police can conduct a free and fair probe.
Nagar represents the Dudu constituency in Ajmer district in the state assembly.
A police officer said the woman had approached a court which directed the police to register the FIR against the minister.
