Emergency services were called to the scene of Stratheden Road and Langton Way in Blackheath near Shooters Hill to an altercation on a bus.
Police discovered a 24-year-old man who had sustained a stab wound.
He was taken to hospital where his injuries were assessed to be not life-threatening or life-changing.
A man in his 40s was arrested on suspicion of grievous bodily harm and was taken to hospital for treatment.
He currently remains in police custody.
A third person – a police officer – also sustained injuries caused by glass and received medical treatment.
A crime scene is in place.
A spokesperson for Metropolitan Police said: “Police and the London Ambulance Service were called shortly after 04:30hrs on Sunday, 30 March to reports of an altercation on a bus in Stratheden Road/Langton Way, Blackheath SE3.
“A man aged 24 was found to have a stab wound and was taken to hospital. His condition has since been assessed as neither life-threatening nor life-changing.
“A 40-year-old man was arrested at the scene on suspicion of grievous bodily harm. He was taken to hospital for treatment for a head injury and then taken into police custody.
“A crime scene remains in place at this stage.
“A police officer also received medical treatment for an injury caused by glass at the scene.”
