In an incendiary intervention, Ephraim Mirvis said Labour's handling of the issue, which has dogged the party under Mr Corbyn's leadership, was "incompatible" with British values.
He said the overwhelming majority of Britain's Jews were "gripped with anxiety" ahead of the General Election on December 12, warning "the very soul of our nation is at stake".
Speaking on a visit to West Yorkshire today, Shadow Chancellor John McDonnell defended Mr Corbyn, saying people who criticism the Labour leader over anti-Semitism "need to take cognisance of people who really know" him.
And Michael McGowan, a former Labour MEP for Leeds, said the Chief Rabbi's words were "unhelpful to the Jewish community in the UK and to Israel as a country, and they are damaging to community relations".
He said: "He would do well to reflect on his comments that the Jewish community is seriously considering leaving the country if Jeremy Corbyn is elected Prime Minister.
"He certainly does not reflect the views of the Jewish community in Leeds and it is clear that his knowledge of the Jewish community on the ground is limited ,
"I am surprised that Rabbi Mirvis appears to be unaware that Leeds has an important Jewish community which has enriched the quality of life in our community in industry, politics, education, culture and sport.
"Two out of our current four Labour MPs for Leeds are Jewish: the MP for North East Leeds, Fabian Hamilton, is the shadow minister for peace and international relations and the MP for North West Leeds, Alex Sobel, has a proud record of promoting of co-operative relationships and enterprise.
"As a member of the Labour party all my adult life, first elected a Labour councillor at the age of 21 and an MEP for Leeds for 15 years and member of the European Parliament's delegation for Israel, the Jewish community of Leeds has always enriched my personal and political life.
"I have known Jeremy Corbyn since 1985 when we were both part of the launch of the European refugee support network for the refugees from the Western Sahara and his opposition to all forms of racism and support for refugees, peace, and human rights is a matter of record."
Allies of Mr Corbyn acknowledged that Mr Mirvis had raised a serious issue, but insisted the numbers of those involved represented a "tiny fraction" of the party's membership.
However Mr Mirvis received high-profile backing from the Archbishop of Canterbury, the Most Rev Justin Welby, who said his intervention reflected the alarm felt by many in the Jewish community.
"That the Chief Rabbi should be compelled to make such an unprecedented statement at this time ought to alert us to the deep sense of insecurity and fear felt by many British Jews," he said.
Writing in The Times, Mr Mirvis said "a new poison - sanctioned from the top" had taken root in the Labour Party.
He added: "How complicit in prejudice would a leader of Her Majesty's Opposition have to be to be considered unfit for office?"
Speaking on a train to West Yorkshire, where he will be speaking at a campaign event in the Colne Valley constituency today, John McDonnell told The Yorkshire Post: "Three days ago there were letters in the Guardian which brought together leading members of the Jewish community, many of them have known Jeremy for decades, supporting him and upholding his role in tackling anti-Semitism and applauding him for it.
"I saw that letter and I thought it was admirable because these are real people who have known Jeremy Corbyn for decades.
"Obviously there are different views, they need to take cognisance of people who really know Jeremy."
The controversy erupted as Mr Corbyn prepared to unveil the party's race and faith manifesto - including a commitment to make the Equality and Human Rights Commission, which is currently investigating Labour anti-Semitism, "truly independent".
Asked if the Chief Rabbi's comments would undermine this, Mr McDonnell replied: "No, I don't think so." He added: "They will be taken into account. What we generally try and do is respond to any criticism that comes to us and make sure we always learn lessons for the future."