Some 70 firefighters tackled the blaze at the Baitul Futuh mosque in Morden.
The London Fire Brigade (LFB) sent investigating officers and the incident was referred to the police, according to the Telegraph.
One man in his 40s was taken to hospital after being treated for smoke inhalation.
Roads were closed in the suburban neighbourhood surrounding the mosque, which is thought to be one of the largest in Western Europe.
The mosque was built on the site of the old Express Dairies in 1999.