Police were called to Sydenham Road at 4.02pm on Friday, February 28.
Armed officers attended and arrested the man within 30 minutes on suspicion of possession of an offensive weapon.
He remains in custody, and enquiries are ongoing, a police spokesperson confirmed.
A spokesperson for the Metropolitan Police said: “Police were called to Sydenham Road, SE26, at 16:02hrs on Friday, 28 February, following reports of two people on a moped carrying knives.
“Armed Response Officers attended and arrested a man within 30 minutes on suspicion of possession of an offensive weapon.
“He remains in custody, and enquiries are ongoing.”