The cleric termed her action as "anti-Islamic" and accused her of bringing a bad name to the religion. He also urged Jahan to change her name.
"Worshipping other Gods is not permitted in Islam" and "Islam does not need her," he said.
Accompanied by husband Nikhil Jain, Nusrat offered prayers at Suruchi Sangha Pandal in Kolkata on Sunday. After the prayers, she played 'dhaak' (a traditional Bengali dhol) along with her husband.
Watch: Nusrat Jahan dances, plays dhol with husband on Durga Pooja
“”Nusrat Jahan has performed puja which is totally anti-Islamic. She is not practising Islam. She even married a non-Muslim. Since she does not believe in the Islam, she should change her name. Why is she insulting the Islam?" Mufti Asad Kasmi, vice-president of Itehaad Ulema-e-Hind, was quoted as saying by news agency ANI.
The cleric further said, "The Islam does not need any person who bears an Islamic name but actually defames the Islam."
Earlier this year, Jahan married a non-Muslim businessman, Nikhil Jain.
Soon after their marriage, her wearing a “sindoor” and bangles had also become a subject matter of controversy. A city-based Muslim cleric had criticised Jahan for marrying a Jain and wearing sindoor, calling the practices un-Islamic.