The suspects, aged 19 and 21, were detained following a knife attack in Samos Road, Anerley, at around 12.30pm on Sunday.
A 22-year-old man, who was found by emergency services at the scene suffering from stab wounds, was later pronounced dead.
The Metropolitan Police said enquiries to establish the victim’s identity continue in order to inform his next of kin.
Lewisham West and Penge MP Ellie Reeves said she was “devastated” to hear of what was a second fatal stabbing in her constituency in the space of three days.
“I am waiting for further details but my thoughts are with the victim and their family,” she wrote on Twitter. “This has to stop.”
The killing is the third fatal knife attack in south London in a matter of days, following the death of 15-year-old Jay Hughes in Bellingham on Thursday evening and Malcolm Mide-Madariola, 17, outside Clapham South station on Friday.
Police have yet to make an arrest in connection with either killing.
The latest stabbings come towards the end of what has been a year of violence in the capital, with the Met forced to open more than 100 murder investigations.
London mayor Sadiq Khan has previously blamed rising knife crime on £700m cuts to police budgets in the city over seven years, which is expected to be trimmed further still in coming years.
On Friday, Mr Khan announced the latest measure in the “public health approach” to tackling violence, with a review of the most serious offences since 2014 to discover the trends behind attack.
Met commissioner Cressida Dick said on the same day that forces must focus on “traditional” threats to community safety such as serious violence and drug gangs rather than non-criminal acts of misogyny.