Maryam Hamka, 36, vanished after leaving a Woolworths store on Albert Street, Brunswick about 5.30pm last Saturday, April 10.
Police arrested a 45-year-old man last night following a search warrant at a Brighton property.
He was charged last night with matters unrelated to Ms Hamka’s disappearance.
He has been remanded to appear in Melbourne Magistrates’ Court on April 30.
“We’re very stressed … we just want answers,” Ms Hamka’s sister, Amel Hamka told 9News.
The missing woman’s family said it is unusual for her to not call or check-in on her nephew who she saw almost every day.
Maryam Hamka is described to be 165cm tall, with a thin build and long black hair, brown eyes and an olive complexion.
She was last seen wearing a black dress and had told family she was intending to visit a friend in Brighton.
Ms Hamka was reported missing to police on the Thursday, April 15.
Investigators have released images of her in the hope someone recognises her and can provide information on her whereabouts.