Police were called at 5.30pm on Saturday after a body was discovered near a community centre in Kidbrooke Park Road, Kidbrooke.
A post-mortem examination will be arranged in due course.
At around 9.20pm, police attended an address in Lewisham and arrested a man on suspicion of murder. He has been taken into custody at a south London police station.
A number of crime scenes are in place and enquiries are ongoing.
Anyone with information or any witnesses can call police on 101, reference 5747/18. To remain anonymous, please contact Crimestoppers.