The enquiry was launched on Sunday after the arrest of three members of his family, police sources.
Chief Rabbi Shlomo Amar, one of the most powerful men in the country, will be quizzed on his return from a visit to Thailand after police were given the green light from Attorney General Menachem Mazuz, the sources said.
The rabbi's 31-year-old son Meir Amar was arrested last Thursday for allegedly masterminding the kidnap and beating of the 17-year-old boyfriend - whom his sister Ayala first met through the internet - in a bid to save the family's honour.
Ayala, 18, and the rabbi's wife Mazal were also arrested, although they have since been released on bail.
Investigators believe that Meir Amar, who was estranged from his father, first kidnapped the unnamed youth in northern Tel Aviv by convincing his sister to lure him down to his car.
He then drove him off to a nearby Arab village where he was beaten and even had his kippa (Jewish skullcap) humiliatingly cut in half by two assailants.
A gag order on the case, which dominated the front pages of Israeli newspapers on Sunday, was lifted only at the weekend. 
Rabbi's legal response

The top-selling Yediot Aharonot daily ran an interview with the boyfriend, who said that the rabbi was well aware of what had happened as he himself had seen the teenager after Meir Amar drove them back to the family home after the alleged assault.
The rabbi's lawyers have vehemently denied that he had any involvement in the incident, underlining that Meir had been estranged from the rest of the family for years.
The teenager insisted that he had forgiven Ayala and would like to get back together with her despite everything that had happened.
"I still love her. If she wants to come back, I'll be happy," he told the daily. 
Breaking tradition

The couple, who first communicated on the internet with the nicknames Roni222 and The Lover, had gone on dinner dates and even went hiking together.
With open contact between young men and women frowned upon in ultra-Orthodox, or Haredi society, increasing numbers are looking to find love through the internet.
Rabbis have in the past issued edicts against the use of the internet but attempts for a blanket ban were defeated by popular pressure.