Victoria Police said emergency services attended an address in Village Way, Maribyrnong, 3:45pm on Tuesday and found the body of a 45-year-old woman.
The death is not being treated as suspicious and police are preparing a report for the coroner.
The City of Maribyrnong said the council was "shocked and saddened to learn of the sudden passing" of Cr Carter, who was Maribyrnong's first three-time female mayor.
"Councillor Carter was a trusted and valued colleague and her passing is an enormous loss to our community who she has worked tirelessly to support over her 16 years on Council," the council said in a statement.
Federal Labor MP Tim Watts said he was "devastated" by the death of the former mayor and councillor.
"I had the privilege of seeing first-hand the impact that Sarah had as a councillor and Mayor in Melbourne’s West, as an international aid and development advocate and as a friend. She had an impact on so many ’s lives," he said.
"She gave so much of herself and wanted to give so much more. She’s been taken from us far too soon. It’s a terrible loss to our community and our country."
Cr Carter was serving her fourth consecutive term on the council after being first elected in 2008.
We acknowledge Aboriginal and Torres Strait Islander s as the First Australians and Traditional Custodians of the lands where we live, learn, and work.
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