Ms Nessa was attacked when she made a five-minute walk towards The Depot bar to meet a friend and she never made arrived at the pub.
The 38-year-old man was arrested at an address in Lewisham on Thursday this week.
Detectives have continued their appeal for information about a man seen in CCTV footage in Pegler Square on the evening the primary school teacher was murdered.
Anyone who recognises the man or silver vehicle in the images and CCTV footage released are being urged to make contact with the police immediately.
Detective Chief Inspector Neil John, from the Met’s Specialist Crime Command, said:“We want to thank those who have shared our image appeal over the last 24 hours – it has gained a huge amount of coverage and we are extremely grateful for the public’s help.
“We are now a week on from Sabina’s murder and while we have made good progress with our investigation we must keep this appeal for information going and encourage anyone who has any information to come forward.”
Ms Nessa’s was discovered near the OneSpace community centre within the park at around 5.30pm the following day after the attack.
A post-mortem examination carried out on Monday was inconclusive.
Anyone with information should call the incident room on 0208 721 4266 or Crimestoppers completely anonymously on 0800 555 111.