More than 70 graves have been vandalised in the Russian Orthodox and Serbian Orthodox sections of Rookwood Cemetery, police say.
Police said offenders entered the cemetery via Hawthorne Avenue and desecrated the graves between 9pm on Tuesday and 6am on Wednesday.
Several were pushed over or smashed but no graffiti was found.
Flemington Local Area Command officers are now investigating the incident, including how the vandals were able to enter the grounds.
Duty officer Inspector Craig Miller said police were still determining whether the Russian Orthodox and Serbian Orthodox sections had been targeted.
A Ukrainian community group has labelled the attack a hate crime and called for an investigation "at the highest levels".
"Australians of Ukrainian heritage are sickened by the deplorable destruction of graves at Rookwood cemetery," the Australian Federation of Ukrainian Organisations said in a statement.
The attack came a day before Ukrainian President Petro Poroshenko arrived on a two-day tour of Australia, in which he was set to attend a memorial service with Prime Minister Tony Abbott for victims of flight MH17.
Julie Rusten, who runs tours around the cemetery to raise money for restoration projects with the Friends of Rookwood group, said she was "filled with disgust and despair".
"Whenever there's any kind of vandalism, I feel like grabbing these people by the shirt and saying, 'What if it was your family, what if it was your grandmother's grave?"
Police are urging anyone with information to call Crime Stoppers on 1800 333 000 or to use the Crime Stoppers online reporting page.
Photo: Nick Moir