Police were called at 5.33pm on Saturday, 18 September after a body was discovered near a community centre in Kidbrooke Park Road, SE3.
Officers believe they know the identity of the woman, who is aged in her 20s, but they await formal identification and confirmation that next of kin have been informed.
A post-mortem examination will be arranged in due course.
At around 9.20pm on 18 September, 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.