Warning: Aboriginal and Torres Strait Islander readers are advised this report contains the name and image of a person who has died.

South Australian Police have charged a 37-year-old man with the murder of Indigenous woman Michelle Sumner.

Ms Sumner was found unresponsive at Edwards Park, in Adelaide's southern parklands, on January 20 this year.

Police said Ms Sumner's cause of death was "initially unclear" but that a forensic examination later determined she had died from an assault, the ABC reports.

SA Police said in a statement that the matter was subsequently "declared a major crime and detectives have since worked extensively to establish the circumstances surrounding Michelle's death".

They said the suspect, who was arrested and charged on Monday, and Ms Sumner were known to each other.

Detective Acting Superintendent Andrew Macrae said the arrest "marks a significant step forward in what has been a long and complex investigation".

"We hope today's development offers Michelle's family some measure of comfort," he said.

The ABC reports that the accused man, of no fixed address, was refused bail and is expected to appear in the Adelaide Magistrates Court on Tuesday.

Police have urged anyone with information about Ms Sumner's death to contact Crime Stoppers.