Labour moved to distance itself from a series of pro-Corbyn social media groups after an investigation found they contained hundreds of messages promoting Holocaust denial and hate towards Jews.
Shadow digital minister Liam Byrne admitted there was “real alarm” at the scale of the problem.
Mr Izzard, who has taken a place on the party’s ruling national executive committee (NEC) following the resignation of a Corbyn ally accused of ignoring anti-semitism, said Labour needed to “make amends” to the Jewish community.
He said the issue had to be dealt with “for the good of the people Labour seeks to represent”.
Mr Izzard’s appointment to the NEC followed the resignation of Christine Shawcroft, who quit amid criticism of her opposition to the suspension of a council candidate accused of Holocaust denial.
As the runner-up when she was elected last year, Mr Izzard now automatically takes her place.
“This is a very important time for the Labour Party and we must stamp out completely the stain of anti-semitism from a minority of members. It has no place in our party,” Mr Izzard said.
“We must make amends and repair the damage with the Jewish community as Jeremy Corbyn has promised to do.”
Mr Byrne said Mr Corbyn now needed to make good his promise to Jewish leaders to tackle the issue, pointing to the backlog of around 70 cases of anti-semitism still to be dealt with.
He echoed deputy leader Tom Watson in highlighting the case of former London mayor Ken Livingstone – a long-time ally of the Labour leader who remains suspended over comments suggesting Hitler supported Zionism in the 1930s.
“I personally do not think that Mr Corbyn is an anti-semite, I don’t think he has an anti-semitic bone in his body,” Mr Byrne told the BBC’s The World This Weekend.
“But the reality is now that we need action and not simply words.
“We have got a lot of disciplinary cases stacking up. Mr Livingstone is at the top of that queue.”
An investigation into 20 of the biggest pro-Corbyn Facebook groups by a national newspaper had uncovered routine attacks on Jewish people, including Holocaust denial.
Twelve senior staff working for Mr Corbyn and shadow chancellor John McDonnell were reported to be members of the groups, which contained more than 2,000 racist, anti-semitic, misogynistic, violent and abusive messages.
A Labour Party spokesman said: “These groups are not run by the Labour Party or officially connected to the party in any way.
“The Labour Party is committed to challenging and campaigning against anti-semitism in all its forms. Any complaints of anti-semitism are taken extremely seriously.
“These are fully investigated in line with our rules and procedures and any appropriate disciplinary action taken.”