Authorities were "selectively and viciously cracking down on Muslims who dare to speak up... against the discrimination faced by them," Amnesty's Aakar Patel said in a statement.
"Cracking down on protesters with excessive use of force, arbitrary detention and punitive house demolitions... is in complete violation of India's commitments under international human rights law."
More than 300 people have been arrested in the northern Uttar Pradesh state for joining last week's rallies.
The state's chief minister, firebrand monk Yogi Adityanath, is one of India's most prominent Hindu nationalist politicians, known for sectarian rhetoric against India's 200-million strong Muslim minority.
Adityanath has repeatedly called on authorities to demolish the homes of people accused of crimes, an exhortation critics say violates constitutional and human rights law prohibitions on collective punishment.
Amnesty has demanded an "immediate and unconditional release" of detained protesters, and Patel said the arrests and demolitions were "part of an alarming escalation of the states' measures targeting Muslims".
Since coming to power nationally in 2014, the Bharatiya Janata Party (BJP) has been accused of championing discriminatory policies towards Muslims.
Prime minister Narendra Modi's government proposed a controversial law that granted faster citizenship to refugees in India, but not if they are Muslim, while state BJP governments have passed laws making inter-religious marriages harder.
Cities around India saw sizable demonstrations on Friday, with some crowds burning effigies of Nupur Sharma -- the BJP spokeswoman whose comments during a TV debate show set off the furore.
Sharma has been suspended from the party, which issued a statement saying it respected all religions, while the governments of nearly 20 Muslim-majority countries called in their Indian envoys to register their disapproval.
Friday also saw huge protests in neighbouring countries, with police estimating more than 100,000 people mobilised across Bangladesh after midday prayers.
Another 5,000 people took to the streets in the Pakistani city of Lahore, demanding that their government take stronger action against India over the comments.