The incident took place on December 26 2017 when Shubam Verma asked the victim to meet him at a guest house in Noida's Sector 26, on the pretext of marrying her the next day, they said.
"The accused also made an MMS clip, and uploaded it on social media," a police official said.
The woman, who hails from Rajasthan's Sikar district, is a professor at a medical college in Kanpur and was friends with Mr Verma since their college days.
The woman has now been sent for a medical examination. A case has been registered and the police has launched a probe to hunt down the accused.