In comments responding to remarks made by the UK's Chief Rabbi Ephraim Mirvis who criticised alleged antisemitism in the Labour Party, the MCB said that British Muslims should "listen" to Mirvis "and agree on the importance of voting with their conscience".
The spokesperson added that the chief rabbi's comments "highlighted the importance of speaking out on the racism we face, whilst maintaining our non-partisan stance".
They also agreed with Mirvis that "some politicians have shown courage but too many have sat silent".
However, the MCB also launched a scathing attack against Britain's ruling Conservative Party, accusing the Tories of approaching the issue of “Islamophobia with denial, dismissal and deceit” and claiming that they had a "blind spot for this type of racism" and failed to take any steps towards solving it.
"It is abundantly clear to many Muslims that the Conservative Party tolerate Islamophobia, allow it to fester in society."
The Conservative Party leadership has pledged to open an inquiry into Islamophobia in its own party before the year's end.
A Conservative Party spokesman said:
"We celebrate and value the contribution Muslims have made and continue to make to our great country. We actively support freedom of worship and the role of faith in public life. Our manifesto has committed to ensuring everyone’s rights are respected and everyone is treated with fairness and dignity", he added.
"We are already establishing the terms of an investigation to make sure that such instances are isolated and robust processes are in place to stamp them out as and when they occur."
The statement comes as Britan's Chief Rabbi Ephraim Mirvis strongly criticised the Labour party on Monday for the issue of alleged antisemitism within the opposition party, saying that "a new poison - sanctioned from the very top - has taken root".
He also said that Labour leader Jeremy Corbyn's claim of having attempted to remove antisemitism from the party was "mendacious fiction".
The announcement came just before Corbyn spoke at the party's race and faith manifesto launch, where he said that anti-Jewish racism was "vile and wrong" and that no future Labour government would permit it.
Accusations of antisemitism have plagued the Labour Party since the election of Jeremy Corbyn in 2015, seeing some MPs leave the party over the issue.
However, Corbyn has said he is making efforts to respond to the problem, releasing an educational webpage earlier this year on combating anti-Jewish racism.