The FIR was lodged by Gomti Nagar police on the complaint of IPS officer Amitabh Thakur, police sources said here.
In his complaint, Thakur alleged that the songs were "extremely vulgar, lewd and indecent and act as an offensive catalyst for crime against women".
The FIR has been registered under sections 292, 293 and 294 of the IPC that are related to obscenity offences.
28-year-old Honey Singh raps mostly in a mix of English and Punjabi and has lent his voice in recent Bollywood films like 'Khiladi 786', 'Cocktail' and 'Luv Shuv Te Chicken Khurana'.
Outrage against the rapper and his derogatory songs have been pouring on social networking sites like Facebook and Twitter for the past few days.