The constable has been suspended, while a woman dance instructor who was also allegedly involved in the crime is absconding, SSP Shalabh Mathur said.
The businessman, Arpit, was allegedly invited by the instructor to her flat in Barra area yesterday, where she clicked obscene pictures of him with some girls from her troupe.
She, along with the constable, Manoj Gupta, who was also present there, allegedly threatened to make the businessman's images public if he did not immediately cough up Rs 2 lakh.
The man then called up his family and asked them to come to the area with the money.
Efforts are on to arrest the others, police said.