Officers were called to Sandcroft Court in Battersea at around 2am on July 12.
The early morning incident led to one man being hospitalised but his condition is not life threatening.
The arrested individuals remain in custody as enquiries continue.
Following the incident, a Section 60 was granted for July 14, from 7pm to 7am, to ensure public safety.
Section 60 of the Criminal Justice and Public Order Act 1994 allows a police officer to stop and search a person without reasonable suspicion.
A spokesperson for Metropolitan Police said: “Police were called at 0200hrs on 13 July to a group of males fighting with knives in Sandcroft Court, Battersea.
“Officers attended along with LAS. One man was taken to hospital; his condition is not life-threatening.
“Nine males were arrested in connection with the incident. They have been taken into custody.
“Enquiries are ongoing to establish the circumstances.
“A Section 60 has been authorised following the incident.
“This will be in effect from 1900hrs to 0700hrs on 14 July as officers work to keep people safe.”