The confrontation in South Yarra happened on Tuesday afternoon, just days after Islamist group Hamas launched an attack on Israel from Gaza, triggering racial tensions around the world.
"There is absolutely no place at all in our society for anti-Semitic or hate-based behaviour," Victoria Police said in a statement on Wednesday.
Melbourne Crime Investigation Unit detectives are investigating.
Anti-Defamation Commission chair Dvir Abramovich said he was deeply shocked and the incident should set alarm bells ringing.
"No wonder the Jewish community feels under siege, I am profoundly worried that the massacres carried out against Israelis will now lead to harassment, violence and even worse here in our city," Dr Abramovich said.
"The ugliness of anti-Jewish hatred is exploding and people are scared that they will beaten and brutalised on the streets and in their businesses."
He called on the state government and police to continue to respond to hate and stamp out targeted attacks.
Liberal senator for Victoria Sarah Henderson called the South Yarra incident abhorrent and said there had also been reports Jewish families in Melbourne were fearful of sending their children to school.
More than 1000 people attended a pro-Palestine rally outside the Victorian State Library on Tuesday evening, a day after protesters chanted anti-Israel and anti-Jewish rhetoric at a Sydney rally.
Victoria Police said there were no major incidents or arrests at the Melbourne rally, amid a strong police presence.
More than 1000 Israelis, mostly civilians, have died since the attack began on Saturday.
The death toll from Israel's retaliatory air strikes is believed to have killed at least 830 people and wounded 4250 in Gaza.
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