The far-right activist, whose real name is Stephen Christopher Yaxley-Lennon, tweeted that the place of worship “has a long history of creating terrorists and radical jihadists”.
He later responded to criticism, adding: “Facts are facts. I didn’t create this mosque’s history.”
Read more about the Finsbury Park mosque attack
Responding to Robinson on Twitter, one angry user said: “Does that make it OK then? Because that’s exactly what it sounds like you’re trying to say.”
Another added: “Sorry but what on earth does this have to do with the fact that innocent lives were lost? Are you trying to justify these acts?”
The attack took place outside the Muslim Welfare House, a few hundred metres away from Finsbury Park Mosque.
The mosque once became known as a “haven” for extremists, when radical Islamic cleric Abu Hamza was iman there between 1997 and 2002.
However, it was raided and shut down by police in 2003. Since then it has been run with a board of trustees supported by the Muslim Association of Britain (MAB).
In November 2014, it was given a Visible Quality Mark by national body Community Matters for stamping out extremism.
A spokesperson for HopeNotHate said: “The problem with ‘Tommy Robinson’ is that he gravitates around these incidents like a carrion crow, waiting to pump out his message of division and civil strife and blaming all Muslims for the actions of a few.
“Far from being the answer, Robinson is very much part of the problem. Pushing out messages attacking Muslims is hardly likely to take down the temperature: in fact, the very opposite. Those who push anger and hatred should look closely into their consciences when that is reflected back on the streets.”
Just a few weeks ago, Robinson said militias would be set up to “clean out this Islamic problem” in comments many said were inciting racial hatred.
He was widely condemned for launching into a rant about Islamic extremism moments after the Westminster bridge attack.
The former British National Party member has attempted to shake off his far-right image and ties to football hooliganism after leaving the EDL in 2013.
Robinson joined think tank Quilliam to discuss “alternative ways” of tackling extremism in the UK, but last year announced he was to become the UK co-ordinator for the anti-Islamist movement Pegida, which was founded in Dresden.
Josef Schuster, chairman of the Central Council of Jews in Germany, has described the group as a mix of “neo-Nazis, far-right parties and citizens who think they are finally allowed to show their racism and xenophobia openly.”