According to Modena prosecutors' initial findings, the father Ahmad Khan Butt, a 53-year-old construction worker, threw his wife to the ground and beat her with a brick while the brother Umair attacked his sister.
"The victim did not want her daughter to have an unhappy relationship like the one that had been forced on her," said deputy Modena prosecutor Lucia Musti, who is in charge of the investigation.
"The mother and the daughter were on the same side and this could be called a 'cultural' homicide because in addition to domestic violence there is the issue of the traditions that may have motivated the crime," Ms Musti said.
The family's three other children have been taken in by Italian social services.
The Italian political class reacted with indignation at the incident which was highly similar to the cases of a girl of Pakistani origin in 2006 and a Moroccan girl in 2009 who wanted to lead Western lives with Italian boyfriends.