He later apologised for the remark.
According to the Times, the minister may be barred from entering the country.
The Home Office said it exercises such powers “when the purpose of someone’s visit to this country is to spread hatred”.
A Home Office spokesman told the JC: “This Government upholds free speech but we will not let it be used to excuse detestable views that directly contravene our values.
“We take the threat from extremism seriously and we will challenge it wherever we see it.”
Sara Khan, the anti-extremism tsar, warned that his “appalling statements, including towards his fellow Jews” would have a divisive impact on society.
She added: "This kind of divisive rhetoric has a real impact on individuals, communities and wider society. I hope he gets the message that his abhorrent views aren’t welcome.
“This kind of divisive rhetoric has a real impact on individuals, communities and wider society. I welcome the robust response to this rabbi from both local organisations and national leaders in the Jewish community."
Rabbi Mizrachi is expected to land in the UK on Wednesday.
A number of controversial figures have been banned from entering Britain in recent years.
In 2010, Indian Muslim preacher Zakir Naik, was denied entry by then-Home Secretary Theresa May after he claimed "every Muslim should be a terrorist", according to the Independent.
Last year, anti-Islam commentators Brittany Pettibone, Martin Sellner and Lauren Southern were also barred.
At the time, the Home Office said: “Border Force has the power to refuse entry to an individual if it is considered that his or her presence in the UK is not conducive to the public good.”
Despite a number of venues cancelling appearances, Rabbi Mizrachi’s planned appearance at the Beth Hamedrash Knesset Yehezkel shul in Golders Green, led by Rabbi Aharon Bassous, will go ahead.
In response, the Charity Commission has said it will “engage with the trustees of Beth Hamedrash Knesset Yehezhel… to determine whether this gives rise to regulatory concerns”.
A Charity Commission spokesman said: “Trustees should ensure all their charity’s activities further their charitable purposes and mission”.
In its official guidelines, the Charity Commission advises trustees they must not “promote extremist views or activity”.
It reads: "Concerns about a charity involved in supporting, or giving a platform to, inappropriate extremist views, would call into question whether what it was doing was lawful, supporting its purposes and for the public benefit.
"Even where certain views fall below the criminal threshold… if they are harmful to social cohesion… these may also be inconsistent with the public benefit requirement.
"Where speech is lawful, you should consider the risk of damage to charity’s reputation that could be caused by inhibiting free speech."
