Fire crews reported they had seen the letters EDL scrawled on the side of the building as they battled the blaze at the centre in Muswell Hill.
Scotland Yard said it was treating the fire at the Somali community centre as suspicious and announced that the Counter Terrorism Command was leading the inquiry.
Fire crews were called to the Somali Bravanese Welfare Association in Coppetts Road at 3.15am and took nearly an hour and a half to get the blaze under control.
The two storey building, which also houses the Al-Rahma Islamic Centre and is listed as a mosque, was completely destroyed in the fire.
If confirmed as arson the incident would be the most serious so far in a series of attacks on mosques in the UK since the murder of Drummer Lee Rigby in Woolwich two weeks ago.
Barnet borough commander Adrian Usher said: “I have spoken to community leaders and assured them that a thorough investigation is being conducted.
“The safety of our communities is always our priority and we are consulting widely, offering our support and reassurance. All communities can be confident that they have our support and I can be contacted personally to answer their concerns.”
London Fire Brigade said six engines and around 35 firefighters fought the blaze but the two storey building was severely damaged and part of it collapsed.
One woman from a nearby property, in Muswell Hill, suffered shock and was treated at the scene, London Ambulance Service said.
One witness, who wanted only to be known as Nurein, said: ” I was woken up by loud noises and then soon I could smell the fire. I went outside and it was really bad. There were huge flames and lots of smoke. There were several fire engines and I think even a helicopter. It was terrible. This will really shake the community up.”
Mohamed Ali of the Somali charity BritSom said he believed the incident was linked to the Woolwich attack.
He said : “The place has been absolutely destroyed. The community is shocked and very distressed because they have been here in peace for the past 20 years.
“We are a peaceful community so I do not know what has brought this on. The building is a centre for the comunity, it is used as a mosque, a gathering place for Somalis to meet up and as a school for young children to learn Arabic.
“This is shocking but it will not break the community as a whole, I would appeal to the people who did this to to come and sit fown with us and have a dialogue. That is the only way forward.”
Local Conservative MP Theresa Villiers, who represents Chipping Barnet, said: “I am shocked by this attack in my constituency. This kind of hate crime is absolutely despicable. This is not just an attack on the Muslim community. It is an attack on all of us and our values.
“We are a highly diverse multi-ethnic borough with excellent community cohesion in Barnet. We should under no circumstances allow violent extremists to divide us with this kind of outrage.
“I am deeply concerned about the impact this disgraceful crime with have on those who use the Bravanese Islamic Centre. They have all my sympathies at this difficult time.“
The last person left the centre at about 8pm last night, a senior youth worker said today.
Ahmed Ali said when he arrived at 4.15am the building was virtually destroyed and the only apparent evidence of the arsonists were the letters “EDL” daubed in dark spray paint on a wall.
Mr Ali said: “We’re gutted and shattered today, it’s heartbreaking.
“We are in total shock that this has happened in our community, but it will not stop us.
“All our neighbours have shown solidarity today and have been inviting us in for coffee and asking how they can help us rebuild.”
He added: “We were horrified at the death of Drummer Lee Rigby.
“We’re a peaceful community, but the people who did this just have hatred inside.”
The Board of Deputies of British Jews said it was shocked to hear of the incident and expressed its solidarity with the Muslim community. Vivian Wineman, president of the Board, said: “Attacks of this nature are an affront not only to the Muslim community, not only to all minority groups but to all decent people in this country”.
Police were also called to the Bomber Command memorial in Green Park where graffiti demanded that the killers of drummer Rigby should be hanged. It was also defaced a week ago when the word Islam was spray painted on a wall.
Faith Matters, a group which monitors anti-Muslim hatred, said recently that there had been ten attacks on mosques since the Drummer Lee Rigby was killed in Woolwich two weeks ago today.
The most serious so far has been the attempted fire bombing of the Grimsby Islamic Cultural Centre while people were inside.
Yesterday Assistant Commissioner Cressida Dick, who is in charge of the UK’s anti-terror operations, said the backlash against the Woolwich attack in London had not been as serious as police had feared.
She said there had been eight potentially Islamophobic incidents in London in the last two weeks compared to one a day in the previous 12 months.