Angelo Loras, 34, from Toongabbie in NSW, was arrested in Melbourne's CBD on Saturday night, about 24 hours after the front doors of the East Melbourne Hebrew Congregation were allegedly set alight, forcing 20 people to flee.
He has been charged multiple offences including reckless conduct endangering life, criminal damage by fire and possession of a controlled weapon.
The 34-year-old appeared in Melbourne Magistrates' Court on Sunday, where the court was told it was his first time in custody.
He was remanded until a hearing on July 22.
Detectives will investigate the accused man's intent and ideology to determine if the incident was an act of terrorism.
Police are also investigating another alleged act of anti-Semitism on the same night, when protesters who splintered from a larger demonstration allegedly smashed a window, flipped tables, threw chairs and chanted "death to the IDF" outside Israeli restaurant Miznon.
Hours later, offenders spray-painted three cars and a wall outside a Greensborough business in Melbourne's northeast before setting fire to the vehicles, destroying one and damaging two.
Police have revealed they are investigating a fourth incident where offenders used stencils to spray paint offensive images on pillars at a busy intersection and a number of walls in Elsternwick.
It came as hundreds gathered for a pro-Palestine rally in Melbourne on Sunday.
Israeli prime minister Benjamin Netanyahu has condemned "reprehensible anti-Semitic attacks" on both the Melbourne synagogue and restaurant.
He urged the federal government to "take all action" against those responsible.
None of the incidents have been declared terrorism-related but the force is increasing patrols around the synagogue and in the city's southeast.
Home Affairs Minister Tony Burke, former attorney-general Mark Dreyfus and Melbourne MP Sarah Witty met with the synagogue's Rabbi Dovid Gutnick, president Danny Segal and his wife on Sunday morning.
Mr Burke and Mr Dreyfus described the firebombing as an "attack on Australia" and the entire community.
Mr Burke stopped short of declaring the alleged arson attack an act of terrorism, saying it would be up to Victoria Police to decide.
He refused to be drawn on Israel Prime Minister Benjamin Netanyahu's demand the Australian government "take all action to deal with the rioters to the fullest extent of the law".
Mr Burke said he spoke with the Israeli Ambassador to Australia Amir Maimon on Saturday night as news filtered through of plans for him to fly from Sydney for the Sunday's meeting.
The ambassador took it as a signal of the government taking Friday's attacks very seriously, Mr Burke said.
Prime Minister Anthony Albanese condemned the synagogue arson as a "cowardly" act of violence and anti-Semitism and said the attacks on the restaurant and business were unacceptable.
The federal government has offered federal police and security and intelligence agency support to investigators.
"Those responsible for these shocking acts must face the full force of the law," he said.
Victorian opposition police spokesman and Jewish MP David Southwick criticised Premier Jacinta Allan, who condemned the attacks in a statement, for not fronting the media over the weekend.
"Where is the premier," he asked.
"The Jewish community feel like there is a war zone here in Melbourne."
Ms Allan is expected to visit the synagogue on Monday.
The attacks come seven months after a blaze destroyed two buildings at the Adass Israel Synagogue in the city's south and forced worshippers inside to flee.
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