Mr Umunna told Parliament’s The House magazine: “I don’t think we have a problem with antisemitism as a party.
“I think there is a problem with antisemitism on the fringes of the left, there is no doubt about that; it would be completely disingenuous to deny that.”
He said hatred and racism of any variety required a “zero tolerance policy”.
His comments come as the results of an investigation into allegations of antisemitism at Oxford University’s Labour Club are due to be announced.
It is believed that two of the club’s members, possibly aligned to the left-wing grassroots Momentum movement, have been questioned. Momentum has denied its members were involved.
Mr Umuna singled out former London mayor Ken Livingstone, saying the Labour veteran was “the obvious example” of someone who had offended Jews.
Asked by the magazine whether Mr Livingstone’s comments on recent issues relating to the party had been helpful, Mr Umunna said: “No.”
“There are some people who have clearly said some things which have very much offended the Jewish community. Ken Livingstone's the obvious example,” he added.
