The incident happened on the busy road outside a Starbucks at around 1pm today (October 6).
Pictures from the scene show blood on the pavement outside the shopfront of the coffee shop.
Alongside it are bits of clothing scattered on the floor.
A man, in his 20s, was treated at the scene for a stab wound.
He was taken to hospital, where his injuries were assessed as non-life-changing and non-life-threatening.
No arrests have been made at this stage.
The cordon has been placed along some of the shops in the area, but shops such as Leyland SDM remain open despite being within the taped-up section.
Pedestrians in Streatham are having to walk on the edge of the pavement or the road itself as the entire pavement has been blocked off by police.
Officers are extending the crime scene line to the Superdrug entrance, but customers can still go into the store at the time of reporting.
