The man was arrested at an address in Dalston, east London, at around 1.30pm on Monday.
He has been taken to a police station in south-west London where he remains in custody.
Ms Tudos’ body was found by a member of the public on 27 December in a disused building in Finsbury Park, near to her home.
She had been missing since Christmas Eve
A post-mortem examination took place at Haringey Mortuary and gave the cause of death as a stab wound to the abdomen and a head injury.
The murder investigation being led by DCI Nicola Wall is continuing.
DCI Wall said: “We want to hear from anyone who saw, had contact with, or heard from Iuliana after this time.
“We’d also like to hear from anybody who saw anything suspicious within the park over the Christmas period.”
Friends of Ms Tudos described her as “funny, honest, loving” and “definitely something special”.
One of Iuliana’s friends, Sonny Webb, told Sky News she was “like my little sister”.
“She was a lovely person to be around,” he added, “a caring person. She meant so much to me and the world is not going to be the same without her.”
Haringey Borough Commander Detective Chief Superintendent Des Fahy said that extra officers had been deployed to reassure the public.
He said: “We understand that the local community might have concerns, but I want to reassure people that incidents of this nature are incredibly rare.
“We have police out and about on patrol and local Neighbourhood Policing Teams have been out speaking to members of the community.
“By all accounts, Iuliana was a bubbly lively girl enjoying a fun life in London when she was tragically taken from her loved ones. Our hearts go out to them.”
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:: Anyone with information should call the incident room on 0208 785 8244, or contact Crimestoppers, anonymously, on 0800 555 111.