The incident happened in Swingate Lane at around 8.26pm on Friday (August 22).
A man in his 30s was treated at the scene before being taken to hospital by London Ambulance Service crews.
His injuries are not thought to be life-changing.
A 54-year-old man has been arrested on suspicion of grievous bodily harm and remains in police custody.
A Metropolitan Police spokesperson said: “Officers were called by the London Ambulance Service at 20:26hrs on Friday, August 22, after reports of a man with stab wounds in Swingate Lane, Plumstead.
“A man in his 30s was taken to hospital by the London Ambulance Service, his injuries are not thought to be life-changing.
“A 54-year-old man has been arrested on suspicion of grievous bodily harm and remains in police custody.”