The passage in Dawkins' book, The God Delusion, reflects a centuries-old anti-Jewish attitude, Chief Rabbi Sacks said.
Prof Dawkins dismissed the allegation as "ridiculous".
The exchange took place at the BBC's RE:Think festival in Salford during a debate about science and religion.
The dispute began with Prof Dawkins' claim that a controversial passage from his 2006 book was intended to be "humorous".
"The beginning of chapter two, which says the God of the Old Testament is the most unpleasant character in all fiction, that's a joke," he said in the early stages of the debate.
Later Chief Rabbi Lord Sacks said that Dawkins had misunderstood sections of the Hebrew Bible, which are also part of the Christian Old Testament, because he was a "Christian atheist" rather than a "Jewish atheist".
It meant that Dawkins read the Old Testament in an "adversarial way," he said, something that was "Christian" because the faith's New Testament was believed to have "gone one better".
"That's why I did not read the opening to chapter two in your book as a joke, I read it as a profoundly anti-semitic passage."
The text was read out loud by Lord Sacks at the debate.
It described "the God of the Old Testament" as a "vindictive, bloodthirsty ethnic cleanser" as well as "misogynist", "homophobic", "racist", "pestilential" and "infanticidal".
"How you can call that anti-semitic, I don't even begin to understand. It's anti-God," said Prof Dawkins.