Single mum faces court accused of killing elderly woman and allegedly wrapping her body in plastic before dumping it in Melbourne's Maribyrnong River

A woman accused of murdering an elderly woman and dumping her body in a river has appeared in court

The woman, 49, appeared in the Melbourne Magistrates' Court on Wednesday where her lawyer Sharon Healey successfully asked the court to suppress her client's identity.

Reporters were ejected from the courtroom to allow the alleged killer's lawyer to address the magistrate in private about protecting his client.

The woman was arrested on Tuesday after the body of a elderly woman was found with a bag tied over her head and her legs bound by plastic in the Maribyrnong River.

The unidentified woman's body was discovered floating in the river in Flemington on Sunday morning by a local fisherman who said the woman was badly bruised.

Homicide Squad detectives arrested the single mother and a 15-year-old boy from West Footscray, with the pair were both interviewed by police.

While the boy was released without charge, the woman was charged with murder and remanded in custody to appear.

Police believe the women were known to each other.

The matter is scheduled to return to court on Tuesday where media organisations will fight the court-imposed gag order. 

Meanwhile, detective are continuing to appeal for anyone with CCTV or dashcam footage from the areas around Glasmis Rd in West Footscray or Smithfield Rd in Flemington near Lynchs' Bridge between 12pm on July 12 and 10.30am on July 14 to come forward.

'Police are also keen to speak to anyone who may have witnessed any suspicious activity in those areas during that time,' they said in a statement.

Detectives are also investigating the discovery of a man's body, which was found floating in the same river just 90 minutes prior in Footscray.

Police have confirmed the man's death is not linked to the death of the woman and is not being treated as suspicious.

He is yet to be formally identified.

Anyone with information about these incidents is urged to contact Crime Stoppers on 1800 333 000