The incident happened at about 10.50 a.m. on Kennington Road, near the Imperial War Museum, Xinhua reported.
According to the London Ambulance Service, its medical staff treated 32 patients in total, of whom 25 sustained cuts and bruises in the accident. Five suffered more serious injuries, such as head and leg injuries.
Two other patients, a man and a woman, who were trapped on the upper deck in the bus for around two hours, suffered serious leg injuries.
The tree became embedded into the front of the bus and emergency services had to use specialist equipment to access one side of the vehicle, The Independent reported.
The collision was a "particularly nasty" crash and crews worked in "very challenging circumstances" to get the passengers off the bus, said London Fire Brigade Station Manager Clive Robinson, who was at the scene.
The cause of the accident, however, could not be immediately ascertained, said police, adding closed-circuit television footages from inside the bus were being viewed.