Firefighters used specialist equipment to free Dariusz Naidek, 28, following the accident at Balham Mosque.
Mr Naidek, who has lived in Tooting Bec for two years, was trapped by his legs after bricks fell on him.
London Fire Brigade worker Angus Sangster said Mr Naidek was conscious when he was freed and taken to hospital by the London Ambulance Service.
Mr Sangster said: "Forty firefighters worked in very difficult conditions for two-and-a-half hours to release him.
"The building will be handed over to the owners to shore up. An investigation has been launched."