The youths, aged 16 and 14, were arrested earlier on Sunday on suspicion of arson at the Baitul Futuh Mosque in Morden.
The blaze at the mosque, said to be the largest in western Europe, was tackled by 70 firefighters.
An administration building was badly damaged but not the mosque, 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.
The brigade was called at just after 12:00 BST on Saturday to the mosque, which also has a community centre attached.
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."
The two arrested teenagers remain in police custody at a south London police station.
Two teenage boys have been arrested in connection with a fire at a mosque complex in south London.