The victim, aged in her 20s, was discovered in parkland off Kidbrooke Park Road in the Royal London Borough of Greenwich on Saturday.
Police said they were called to the scene close to the OneSpace building at 5.32pm.
The suspect was arrested in Lewisham a few hours later at around 9.10pm. He remains in custody for questioning.
"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," the Metropolitan Police said in a statement.
"A post-mortem examination will be arranged in due course."
The force added that an investigation had been launched and several crime scenes were in place. Officers were seen standing guard near a blue tent.
Detectives are also investigating the death of a man outside Belvedere railway station on Saturday night.
Police were called at around 10.13pm after the victim, aged in his 40s, was found critically injured with suspected stab wounds.
He was pronounced dead at the scene but has not yet been formally identified.
The Metropolitan Police have launched a murder investigation. No arrests had been made by Sunday afternoon.
Anyone with information or any witnesses can call police on 101 or Crimestoppers on 0800 555 111.