Victoria Police missing persons squad detectives arrested the man in Doncaster on Sunday afternoon.
A police spokeswoman said the man is currently “assisting police with their enquiries”.
The spokeswoman said Ms Zhang’s disappearance “is considered to be extremely out of character and police have strong concerns for her welfare”.
Ms Zhang was last seen wearing a pink pyjama top and shorts, and no shoes.
She did not have any personal belongings with her, except for her mobile phone.
Detective Inspector Andrew Stamper, of the missing persons squad, said on Saturday that Ms Zhang’s boyfriend, Joon Seong Tan, 35, of Doncaster, also known as Sam, had been “actively avoiding” police since Thursday.
Mr Tan had told police that he last saw Ms Zhang leave home to go on a walk, but Detective Inspector Stamper said this was unlikely as Ms Zhang would not have left her son in the care of someone who was not an immediate family member.
Detective Inspector Stamper said the disappearance had triggered “a great deal of concern” and talk on social media channels among the Chinese-Australian community.
Anyone with information should contact Crime Stoppers on 1800 333 000.