Police were called by London Ambulance Service at 12.18am on Sunday to a report of male with stab injuries in the More London Riverside area.
Officers found a 19-year-old man suffering stab injuries. He has been taken to hospital.
"While we await a full assessment, his condition is not believed to be life-threatening," said the Met in a statement.
An investigation is under way to establish the circumstances. Police cordons were put in place at several locations overnight but have now been lifted.
No-one has been arrested in connection with the incident.
Any witnesses, or anyone with information that may assist police, is asked to call 101 quoting reference 127/11april.