According to authorities of the local convent school in Ranaghat sub-division, three-four people broke into the building at around 12:30 am and raped her after gagging her.
They also decamped with Rs 12 lakh kept in the almirah locker after raping the nun.
The nun was taken to Ranaghat Hospital by the school hostel authorities in the morning when the matter came to light.
Chief Minister Mamata Banerjee ordered a CID probe into the incident and promised "swift" and "strongest action" against the culprits.
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"We strongly condemn the incident that took place at the Ranaghat Convent," she said.
"We have ordered a CID probe. The agency will be examining all aspects of this horrific crime. Swift, strongest action to be taken against the culprits," Banerjee added.
A CCTV footage of the building showed three persons who are suspected to be the rapists. Police is investigating.
District Magistrate P B Salim, who rushed to the spot, told PTI it was a heinous act and police were already on the lookout for the gang members. "We are yet to get a full picture of the incident," the DM said.
State Urban Development Minister Firhad Hakim termed it as an "attack on humanity" and also sought to link it to Sangh Parivar's 'Ghar Wapsi' programme.
"A religious fanaticism has been created in the country. Different churches are being attacked at various places. In the name of 'Ghar Wapsi', people are being religiously provoked," he said.
BJP leader Sidharth Nath Singh, while condemning the incident, said it reflects the law and order situation in the state.