The arrest was made after a complaint which was lodged with Taltala Police Station.
An Instagram handle with username Kirtisocial had shared three stories about the incident with the disclosure of the identity of the victim.
The arrested person had also issued life threats to the Chief Minister on her Instagram handle.
The person will be produced before the court.
More than a week ago, the news of the rape and murder of the junior doctor was reported from RG Kar Hospital bringing the state administration under scanner over the alleged cover-up and fishy investigation by police before the case was handed over to the Central Bureau of Investigation by the Calcutta High Court.
Though the Kolkata Police has arrested one civic volunteer- named Sanjoy Roy- in a quick response to the crime, doctors who are on strike as a protest suspect there were more involved in the incident.
The hospital's initial message to the victim's parents that their daughter committed suicide and the renovation work near the crime scene within hours after CBI's takeover of the case have raised doubts over the state administration's intent.