As Governor-General Sam Mostyn delivered her speech in the upper house on Tuesday for the opening of the 48th parliament, Senator Faruqi held a sign that read: "Gaza is starving. Words won't feed them. Sanction Israel".
The government's Senate leader Penny Wong introduced a motion on Wednesday to disapprove of the Greens senator's conduct.
It also requests an apology for "unparliamentary conduct" in addition to not supporting her as a potential Senate representative on any delegation during this term.
"What she wants most of all is attention," Senator Wong said.
"Australians expect us, their elected representatives, to uphold our democratic institutions, to demonstrate a degree of respect for each other as they do, and a respect for our institutions."
Labor and the coalition voted in favour of the sanction, while the Greens and WA senator Fatima Payman voted against it.
Senator Faruqi accused her colleagues of being on the "wrong side of history" for a lack of action against Israel over its response in Gaza following the October 7 attack by Hamas in 2023.
"You are more focused on cracking down on black and brown women," she said, before later accepting calls to withdraw the comment.
"The Greens will not be silent as this genocide unfolds.
"You will not be able to intimidate me or any of my colleagues, and we will never stop fighting for freedom, for Palestine."
Prime Minister Anthony Albanese said people elected to the parliament have a responsibility to act like an adult.
"There's a place for demonstrations, and it's not on the floor of the Senate or the House of Reps, for that matter," he told the ABC.
Coalition Senate leader Michaelia Cash criticised the Greens senator for her "breach of respect".
"It was deliberate, prolonged and clearly intended to politicise a solemn and ceremonial event," she said.
"Rules without enforcement are meaningless ... and institutions without discipline become irrelevant."
Pro-Palestinian protester Shane Bazzi was taken out of the upper house by security guards after he began shouting from the public gallery while the motion was being discussed.
"Shame, shame," he yelled while being removed.
Hundreds of protesters called for sanctions on Israel on the lawns of parliament during its opening with one woman arrested, according to the Australian Federal Police.
