Hundreds of thousands of fans have gathered in the heart of Melbourne's central business district to watch Australia matches at the square since the 2006 World Cup in Germany.
Video of fans celebrating wildly went viral during the 2022 tournament in Qatar when Australia advanced to the round of 16.
A number of incidents soured the celebrations, though, with fans being injured by flares and projectiles.
Fans stormed barricades during the 2023 Women's World Cup semi-final between Australia and England, prompting management to cancel plans to screen the Matildas' subsequent third-place playoff at the square.
"After careful consideration, we've made the decision not to show the World Cup on Fed Square's Big Screen this year," Melbourne Arts Precinct Director and CEO Katrina Sedgwick said in a statement on Wednesday.
"This is due to the behaviour of a small number of people at previous screenings which was simply unacceptable and damaging to Fed Square."
The decision triggered a furious response from Australian soccer pundits and a fans group, who said the majority of well-behaved supporters were being made to pay by a tiny minority.
"The pictures and videos of Fed Square during World Cup 2022 went viral around the world, we want to see this repeated,” Patrick Clancy, chair of Football Supporters Association Australia, told local media.
Football Australia said they were extremely disappointed and urged the Melbourne Arts Precinct to reverse its decision.
"Melbourne is one of Australia's sporting and multicultural capitals, and this decision goes against this tradition," Football Australia CEO Martin Kugeler said.
"Federation Square has created some of the most memorable moments in Australian sporting history, dating back to the Socceroos' historic 2006 FIFA World Cup matches and the 2023 FIFA Women's World Cup.
"We are asking our fans to join us in calling on the Melbourne Arts Precinct and the Victorian government to correct their decision in the best interests of football fans, local businesses and all Victorians."
Australia play Turkey, Paraguay and the United States at the June 11 to July 19 World Cup.