Mr Varshney, a member of the Bharatiya Janata Yuva Morcha, issued the outrageous threat while hitting out at the Chief Minister over police action on a rally held on Sunday to mark Hanuman Jayanti in Birbhum, around 180 km from Kolkata.
Alleging that people were beaten up brutally in a baton-charge by the police, the youth leader described the Chief Minister as a "demon" and said, "When I saw the video, I only had one thought... that if anyone GETS me Mamata Banerjee's head I will give them 11 lakh."
Slogans of "Jai Sri Ram" were raised in the rally which, Mr Varshney claimed, was taken out by devotees not linked to any political party. He accused Mamata Banerjee of "targeting Hindus".
The police had refused permission for the Birbhum rally and allegedly used batons when the procession was about to enter a street locally called the Madrasa Road.
There have been clashes recently during rallies organised in the state to mark Ram Navami and Hanuman Jayanti.
Four people were injured after A bomb was hurled at a Hanuman Jayanti rally, around 40 km from Kolkata.
Swords held up during a previous rally on Ram Navami enraged the Chief Minister, who said, "Some BJP leaders who do not know the culture of Bengal are flashing swords on the streets to intimidate people."