The man was taken to the hospital on Thursday with self-inflicted injuries sustained while in custody.
Agnes, also known as Dora, moved to London from Hungary in 2018 and was last seen in Cricklewood Broadway, Camden on Sunday, May 9.
She is believed to have been a sex worker.
When she went missing, Agnes was in a white coat, ripped light blue jeans and pink trainers.
She is approximately 5ft 5in tall with blonde hair.
The police were searching parks near Ms Akom’s home.
The leading investigator, Detective Chief Inspector Neil John, said: “There are serious concerns for Agnes’ safety, and it is our priority to find her as soon as possible.”