Samantha Fraser, 38, was dead inside her garage on Seagrove Way in Cowes on Monday when police visited to check on her after she failed to pick up her two daughters and son from school.
A post-mortem found “she had suffered assault injuries”, Mr Sheahan said.
A 42-year-old man from Paynesville, in the state’s Gippsland region, who knew Ms Fraser has been interviewed and released without charge.
Detectives are looking at whether there was any interference with the crime scene, and have already spoken with a number of people.
Ms Fraser had dropped her children at primary school, had coffee with friends but failed to attend an appointment at midday, Mr Sheahan said.
More than $22,000 has already been raised for her children and family in an online fundraiser via social media platform, Facebook, which hopes to raise $40,000.
Anyone with information on her movements between 11am and 3.30pm on Monday, or with dashcam or CCTV footage from around the street, have been urged to contact Crime Stoppers on 1800 333 000.
Detectives want to speak to anyone who may have been seen entering the Seagrove Way property the day she died.