The incident happened in College Road just before 11am today (January 17).
Officers and London Ambulance Service crews attended and found a man injured.
He was taken to hospital for treatment where his injuries were assessed as not life threatening.
Another man also in his 20s has been arrested on suspicion of GBH with intent.
He remains in police custody.
Police enquiries into the circumstances are ongoing.
A spokesperson for Metropolitan Police said: “On Wednesday, 17 January at 10:55hrs police were called to a report of a stabbing on College Road, Croydon.
“Officers attended the scene alongside the London Ambulance Service (LAS) who treated a man – aged in his 20s – that was suffering with stab wounds.
“He was taken to hospital for treatment; his injuries are not life threatening.
“A man – aged in his 20s – has been arrested on suspicion of GBH with intent and remains in custody.
“Enquiries are ongoing.
“Anyone with information that could assist police is asked to call 101 or ‘X’ @MetCC and quote CAD 2118/17Jan.
“You can also provide information anonymously to the independent charity Crimestoppers on 0800 555 111.”