It’s believed the thief broke into a home on Buchan Court in Wantirna South, sometime between 3pm on Wednesday, November 5, and 7pm on Thursday, November 6.
Nobody was home at the time.
A number of personal items were stolen, including an Order of Australia medal, and a distinctive Tobruk Rats medal.
The Australian War Memorial says the Tobruk Rats medal is an unofficial medal created during the Siege of Tobruk in 1941 for the Australian soldiers serving there.
Anybody with information is urged to contact Crime Stoppers on 1800 333 000 or online.