The fire, which started at about 00:15 BST, was spotted and quickly put out, and did not spread to the wall itself, according to the community group.
The Metropolitan Police said Fallahi is a dual British and Iranian national.
Commander Helen Flanagan, head of counter-terrorism policing London, said: “This charge marks another step forward in one of the investigations into the series of arson attacks targeting the Jewish community and Iranian diaspora in London.
“We are determined to bring everyone involved in these incidents to justice.”
After the incident, Miga Rally released a statement saying: “The memorial wall is a peaceful place of remembrance, documenting lives lost and ensuring victims are not forgotten.
“Any attempt to damage or desecrate such a site is deeply troubling and an attack on the values of remembrance, dignity and community cohesion.
“We hope those responsible will be identified and held accountable.”
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