The family of an Australian nun killed on Malaysia Airlines flight MH17, which was shot down over Ukraine, has been left devastated after thieves in Melbourne stole personal belongings recovered from the wreckage.

The items belonging to Sister Philomene Tiernan, one of 298 people killed in the tragedy last year, were stolen when her sister's house in Richmond was robbed earlier this month.

Among the stolen items was religious jewellery that Sister Tiernan had carried with her throughout her life as a Catholic nun.

The items had been recovered by Malaysia Airlines and returned to the family just months ago.

Detective Senior Constable Andrew Luke said the stolen items would be of very little value to the thieves, but meant the world to Sister Tiernan's family.

"These items are priceless in the eyes of this poor family but would mean almost nothing to the offenders," he said.

"More than anything we're appealing for the return of those items and they can be dropped off at any police station.

"It's heartbreaking for this family to have to go through something like this and now suffer even more."

The burglary happened at the Palmer Street home between June 13 and 18, while the occupants were on holiday.

Anyone with information is urged to contact police.