The incident happened in Elthorne Park in Hazellville Road at around 8.55pm on November 3.
Officers and London Ambulance Service crews attended and found a woman who had been stabbed.
She was taken to hospital where she remains in a critical condition.
The man, in his 20s, was arrested on Tuesday and remains in custody, the Metropolitan Police confirmed.
A woman in her 50s was also arrested on suspicion of assisting an offender.
Police believe the victim and the arrested man are known to each other.
Chief superintendent Jason Stewart described the arrest as a “significant development” in the ongoing investigation.
“Though a man is in custody, we do understand that this incident has caused extreme concern in the community and we would like to reassure the public there will be extra officers in the area over the next few days as enquiries continue,” he said.
“As our investigation is still ongoing we’d urge anyone with any information or who may have been a witness to please contact us on 101 or online, quoting CAD7669/03NOV. The smallest bit of information could make a real difference.”
