Police are appealing for public assistance to help Rodney, Ann Maree and their newborn baby.
The trio were last seen at the Mercy Hospital in Heidelberg about 2am on Wednesday, 10 July.
Police have concerns as the newborn baby requires medical care and supervision.
Rodney and Ann Maree have links to the Mildura area and there is also a possibility they have travelled to New South Wales, specifically the Wentworth area.
Rodney is about 178cm tall, of heavy build with short dark hair and a goatee style beard.
He was last seen wearing a grey ADIDAS t-shirt, black tracksuit pants and tracksuit top with white shoes.
Ann Maree is about 165cm tall with long black hair in a bun.
She was las seen wearing dressing gown with spots and a black ADIDAS hoodie with stripes down each arm.
Police have released photographs of Rodney and Ann Maree in the hope that someone recognises them.
Anyone with information on their whereabouts is urged to contact Heidelberg Police Station on 03 9450 8000.