Greenwich Metropolitan Police have called the incident in Abbey Wood a “serious assault”.
They said additional search powers have been authorised for Abbey Wood, Plumstead, Glyndon, Woolwich Common, Shooters Hill, Thamesmead Moorings, and Woolwich Riverside.
This includes providing power to stop and search individuals in the local areas.
Greenwich Metropolitan Police said they were called at 10:04pm to reports of a stabbing in Wilton Road, Abbey Wood.
They have confirmed three males were found with stab injuries and taken to hospital.
The men are believed to be aged between teens to early 20s.
The police said the injuries are not thought to be life-threatening at this stage.
So far no arrests have been made.