Muslim groups have called on authorities to take serious action against anti-Islamic attacks and say they fear a wave of reprisals in the wake of the Woolwich murder of Drummer Lee Rigby.
The building was daubed with the letters "EDL", apparently referencing the English Defence League.
The blaze came as the RAF Bomber Command War Memorial in Green Park, central London was defaced again after being attacked by vandals last week, this time with the words "Lee Rigby's killers should hang".
Muslim representatives are pleading with police to clamp down on Islamaphobic attacks, and are appealing for solidarity throughout their communities.
Farooq Murad, secretary general of the Muslim Council of Britain, said: "This is the latest in a series of attacks on Muslim institutions since the horrific murder of Drummer Lee Rigby. The British Muslim community came out in droves to condemn this murder, and it is despicable that Muslims should be held to account and suffer in this way."
He added: "It is time for serious action against such crimes. We had fine and decisive words from our leaders condemning the actions of the English Defence League, now we need a proper response from our police authorities, starting with a national police response to this issue.
"Admirably, local police forces and borough commanders have been liaising with communities. Now we need to hear from the Metropolitan Police Commissioner and the leaders of the Association of Chief Police Officers (Acpo) as to what they will be doing to protect this rise in attacks."
Mr Murad appealed to the media to act responsibly and not "stoke up" anti-Muslim sentiment, and urged Muslim communities to unite.
He said: "We are reminded by the words of Drummer Lee Rigby's family and his Regiment, who have warned against reprisal attacks. In spite of these attacks, we are heartened by the many more acts of solidarity that have taken place. In addition to the hate mail, we have received many messages of support from all faith communities."
The fire in Muswell Hill broke out shortly after 3am and ravaged the home of the Somali Bravanese Welfare Association - also known as the Al-Rahma Islamic Centre - described as a place for learning, cultural activities and prayer.
Scotland Yard said it was treating the fire as suspicious following the discovery of the graffiti, and that specialist investigators would conduct a "vigorous and thorough" investigation into the blaze and examine any potential links between the fire and the graffiti.
Unite Against Fascism, which tackles fascism and racism, has organised a vigil outside the cultural centre from 6pm today and is calling on people from all parts of the community to come together.
The Islamic Human Rights Commission (IHRC) said Muslims were scared and living in fear of a "wave of attacks".
Massoud Shadjareh, chairman of IHRC, said: "Muslims feel scared right now and it is completely understandable.
"Muslims have been physically attacked, mosques burnt down, cemeteries vandalised and social media is full of anti-Muslim hatred and violent threats towards Muslims. More needs to be done to protect the Muslim community."
Fiyaz Mughal, of Faith Matters, a group which monitors anti-Muslim hatred, added: "It is very concerning when we know that, online, there is a huge amount of anti-Muslim hate. We know that. When it moves into the physical world, it is extremely concerning."
Chief executive of the charity Victim Support, Javed Khan, condemned the "abhorrent" attack, adding: "This incident absolutely reinforces that extremism in all forms has no place in our society".
Kevin Carroll, of the EDL, said: "The EDL do not approve of any religious buildings being attacked."