Akeem Moore, 22, was shot in the garden of a house on Eastney Road on Friday 7 October.
London's Metropolitan Police said on Tuesday a 36-year-old man had been arrested on suspicion of murder, attempted murder, possession of a firearm, and perverting the course of justice.
He is currently in custody at a south London police station.
At the time of the killing Mr Moore's mother, Lilian Hinchley-Nelson, appealed for prayers.
"May God give myself and my family the strength and comfort at this time," she said.
