Indian security forces banned gatherings of more than four people in the northern districts of Tripura; It warned against "provocative messages" being spread on social media, and reinforced the security of mosques.
Tripura shares an 850 km border with Muslim-majority Bangladesh; Seven people were killed this month at the hands of a group of angry protesters who vandalized and looted a Hindu temple.
Video footage of the scene of the Qur'an being placed on the knee of a Hindu deity statue sparked anti-Hindu riots in Bangladesh, which soon spread to 12 regions of the country.
India has expressed concern about the unrest in Tripura state, which began on the sidelines of a rally of hundreds of followers of the right-wing Vishwa Hindu Parishad group.
At least four mosques were vandalized, and several Muslim-owned shops and homes were looted in the state ruled by Prime Minister Narendra Modi's nationalist Bharatiya Janata Party.
India's Muslim minority leaders say they have come under increasing attacks since the Hindu Nationalist Party came to power in 2014.