Two boys, aged 16 and 14, were arrested over the blaze at the Baitul Futuh Mosque in Morden on Saturday.
The 14-year-old has been bailed and the 16-year-old was released with no further action.
The Metropolitan Police said the investigation was ongoing but "there is nothing to suggest at this stage that this is a hate crime".
The mosque, which has a community centre attached to it, is believed to be the largest in western Europe.
An administration building at the complex was badly damaged in the blaze, which broke out at just after 12: BST, London Fire Brigade said.
A man was taken to hospital suffering from the effects of smoke inhalation and about 30 others left when the alarm was raised.
About 50% of the building's ground floor was damaged as well as part of the first floor and a section of the roof.
Station manager Philip Morton said: "This was a large fire and our crews worked hard in difficult conditions to confine it to the administrative buildings on the site and thanks to their efforts the mosque itself escaped completely unscathed.
"Throughout the incident we worked closely with the local community to ensure our damage control operations took into account the religious significance of the building's contents."
The 5.2 acre (2.1 hectare) mosque serves the Ahmadiyya Muslim Community and there is space for at least 10,500 worshippers, according to its website.
Rafiq Hayat, national president of the Ahmadiyya Muslim Community UK, said: "By the Grace of God the mosque is safe and unaffected and there were no injuries and no loss of life.
"The fire was contained to the hall at the front of the building and some adjacent offices.
"We are extremely grateful for the support of the local community and leaders."
A suspected arson at a mosque complex in south London is not believed to be a hate crime, police have said.