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Police hold 'significant concerns' for missing Melbourne woman Maryam Hamka

Police are seeking information from the public about Maryam Hamka's disappearance. (Supplied: Victoria Police)

Police in Melbourne have "significant concerns" for a Melbourne woman who disappeared more than a week ago.

Maryam Hamka , 36, of Brunswick, was last seen on April 10 as she was leaving a Woolworths store on Albert Street, Brunswick at 5:30pm.

Ms Hamka told her family she was going to visit a friend in Brighton.

She left her home in Barkly Street, Brunswick, with a bag of clothes and was picked up by a male companion. Police are still trying to confirm who that was.

Ms Hamka was not reported missing by her family for five days after she was last seen.

Detective Inspector Andrew Stamper from the Missing Persons Squad at Victoria Police said Ms Hamka has had a "problematic" relationship with her family.  

"It wasn't unusual for her to be away and not be in contact for several days," Inspector Stamper said.

"But as the days mounted, is my understanding, their concerns were raised and linked with the lack of presence on her phone, social media, that's why the family have finally come to police.

Ms Hamka was last seen leaving a Brunswick Woolworths store at 5:30pm on April 10. (Supplied: Victoria Police)

Police executed a search warrant at an address in Well Street, Brighton on Friday night and arrested a 45-year-old man, who is understood to be a former partner.

He was charged with offences unrelated to Ms Hamka's disappearance on Saturday night, police confirmed.

He has been remanded to appear in court on April 30.

Residents in Well Street would recognise Ms Hamka, Inspector Stamper said on Saturday.

"If they saw or heard anything suspicious, particularly around Saturday evening, the 10th of April into the Sunday morning [we urge them to]  contact Crime Stoppers."

Inspector Stamper said some items had been removed from the house.  

He said officers were reviewing CCTV taken from the supermarket to ascertain if she was with anyone.

Ms Hamka is described as 165 centimetres tall, with a thin build, long black hair and an olive complexion. She was last seen wearing a black dress.

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