The door of the mosque was damaged, with two burnt canisters recovered from the scene. No one was injured.
Mosque leaders expressed their gratitude to neighbors who tried to put out the fire with their coats.
“We cannot thank them enough,” they said.
They added that they had received threats to burn the mosque “for a couple of years, but now the attempt has come.”
Manchester City Council deputy leader Luthfur Rahman described the attack as “a despicable act designed to create fear and hatred.”
The mosque urged the local community to “stay vigilant,” and said “Please do not let hate divide us or win.”
Afzal Khan, the MP for Manchester Gorton, tweeted: “Shocked to hear of the attempted arson at Didsbury mosque last night. Solidarity with our brothers and sisters there. Islamophobic attacks against mosques are on the rise.”
Khan asked people to “stay vigilant” and report such incidents to the police and Tell Mama, a charity that supports victims of anti-Muslim hate.