The property owners in Uttar Pradesh were told to vacate their homes beforehand.
Muslims have been protesting after anti-Islamic comments made by two leading members of the governing BJP.
Police have arrested more than 300 people in connection with the unrest.
The remarks were made by BJP spokeswoman Nupur Sharma during a TV debate in May. The BBC is not repeating Ms Sharma's remarks as they are offensive in nature.
The comments incensed Indian Muslims and outraged more than a dozen Islamic nations. The head of the party's Delhi media unit, Naveen Kumar Jindal, was also expelled for sharing a screenshot of her offensive comment in a tweet.
Their comments - especially Ms Sharma's - led to protests in some states.
The chief minister of Uttar Pradesh state, Yogi Adityanath, then ordered the demolition of any illegal establishments and homes of people accused of involvement in riots there last week, the BJP's state spokesperson said.
One house demolished was that of a politician named Javed Ahmed, prominent English-language newspaper Hindustan Times said. His daughter, Afreen Fatima, is a prominent Muslim rights activist.
Properties of two more people accused of throwing stones after Friday prayers were also demolished in the state.
Mrityunjay Kumar, Yogi Adityanath's media adviser, tweeted a photo of a bulldozer demolishing a building and said: "Unruly elements remember, every Friday is followed by a Saturday."
There has been widespread condemnation of the demolition.