A 26-year-old woman and her two sons, a six-month-old baby and a two-year-old toddler, were stabbed in their home in the Arab city of Tayibe overnight Sunday.
Magen David Adom paramedics who were called to the scene pronounced them dead.
The police arrested the woman's husband and the father of the babies, a resident of the city in his 30s, on suspicion of committing the act.
The Israel Police said forensic investigators are collecting findings as part of the investigation.
About a week and a half ago, a personal security guard of the mayor of Tayibe, Adir Wahib Ghanam, was killed when shots were fired towards his home.
Ghanam was evacuated in serious condition to Meir Hospital in Kfar Saba, where hospital staff later pronounced him dead.
The police and the Israel Security Agency (Shin Bet) arrested suspects in the murder. A gag order has been imposed on the details of the incident.