The teenager was struck as he left Dunraven School in Leigham Court Road, Streatham, at 3.30pm on Wednesday.
He is in hospital surrounded by family in a life-threatening condition, police said.
The attacker is alleged to have hit the boy in the head with the pole before moving on to several other pupils and a teacher.
A 35-year-old man has been arrested on suspicion of grievous bodily harm.
He was treated in hospital for minor injuries after being tackled by a police liaison officer based at the school.
Lambeth Police wrote on Twitter: “A 13yo boy was found with a head injury. He was treated at the scene before being taken to hospital.
“The boy’s condition has been assessed as life-threatening.”