The governing body said it was “extremely disappointed” with the decision by Melbourne Arts Precinct, which cited previous “dangerous” fan behaviour in the square.
“The FIFA World Cup is the biggest sporting event in the world and unites Australia’s multicultural communities, while reinforcing our national identity,” said Football Australia chief executive Martin Kugeler.
“Live sites create iconic moments for Australian sports fans,” he added.
“Melbourne is one of Australia’s sporting and multicultural capitals, and this decision goes against this tradition.”
Katrina Sedgwick, chief executive of the Melbourne Arts Precinct, which manages the square, said the behaviour of some fans led to its decision not to host World Cup watch parties.
“This issue is really with a very small group of fans who, unfortunately, behave in a way that is just antisocial and frankly, dangerous,” she told public broadcaster ABC.
“The challenge is when you have a crowded square with lots and lots of people and people are smuggling in flares,” she said.
Some people were injured by flares in previous World Cup screenings, Sedgwick said.
“I think on the final night of the last Socceroos game we screened, we counted over 100 flares and fireworks that had been let off in the square.”
The Socceroos begin their World Cup against Turkey in Vancouver on June 13, followed by games against co-hosts the United States in Seattle six days later and Paraguay in California on June 25.
Former Socceroo Craig Foster criticised the ban on Federation Square watch parties, posting on social media: “All stakeholders should be working to overturn this absurd decision.”