Officers were called to reports of two men seen with knives in Downham Way near Launcelot Primary School at around 3.50pm on April 17.
The man was later found with stab wounds on the same road.
He was taken to hospital for treatment where his condition was assessed as not life-threatening.
Headteacher of Launcelot Primary School, Ms Osbaldeston, said the school is aware of the incident and that it happened away from the premises at the end of the day in which most children had left.
She said: “We ensured that any remaining children were collected safely from after-school clubs and made arrangements for older children who usually travel independently to be collected by an adult.
“The school is open as normal today.”
Another man was arrested at the scene in connection with the incident and taken into police custody.
Urgent enquiries are ongoing to find a second suspect.
The full statement from Metropolitan Police says: “Police were called to Downham Way, Bromley at about 15:50hrs on Wednesday, 17 April following reports that two men had been seen with knives.
“A further call was received shortly after reporting that a male had been found stabbed on the same road.
“Officers and LAS attended the scene and the man was taken to hospital for treatment. His condition has been assessed as not life threatening.
“One man was arrested at the scene and has been taken into custody.
“Urgent enquiries are ongoing to trace a second suspect.”
