Israeli media had previously reported that Washington would impose sanctions on the battalion over its treatment of Palestinians in the West Bank.
Foreign Minister Katz said on Wednesday during a meeting with Judea and Samaria heads that there was "no such thing as settler violence."
The move by the Australian government comes after allies Britain, the United States, Canada and Japan sanctioned some Israeli settlers in response to the violence in the West Bank.
Violent acts by some Israeli settlers in the West Bank have increased dramatically since last October, said Japan's Chief Cabinet Secretary Yoshimasa Hayashi.
The Biden administration holds Smotrich and Ben-Gvir responsible for undermining security in Judea and Samaria and leading the government's policies in these areas.
The Biden administration is reportedly frustrated with the Israeli government's policy of expanding Jewish settlements in the West Bank, as well as Smotrich's and Ben-Gvir's support.
The synagogue's "services have been regularly disrupted to accommodate often incendiary protests in its immediate vicinity," said the New South Wales Jewish Board of Deputies.
The individuals on the list are members of Tzav 9, an organization that regularly blocks humanitarian aid trucks from entering Gaza.
The US, following the implementation of sanctions, said that the action targets Iran's vast shadow banking system used to support Iran's military.
The Biden administration sanctioned Israeli group Tzav 9 for obstructing aid convoys to Gaza, citing actions undermining peace efforts and humanitarian aid distribution.