While not disclosing the reason, Mr Paulista said Argentina cancelled the match.
"We were prepared, with all the necessary logistics for this game, because we understood that we had to fulfil this contract," he explained.
The official said the CBF was working to find another opponent to take advantage of the FIFA window.
Brazil is also set to face South Korea in Seoul on June 2 and Japan in Tokyo on June 6.
"Conversations are still at the beginning, we will probably find an African team, our suggestion is that we play in Europe," he said.
The event organiser Pitch International confirmed: "Unfortunately, the organisers of the friendly in Melbourne have been informed by Pitch International, the agency that scheduled the game for June 11, 2022, that Argentina is no longer prepared to travel to Australia for the match against Brazil".
Victorian Sports Minister Martin Pakula says the government is “pretty pissed off” Argentina has reneged on its contract to play Brazil in a friendly at the MCG in June. “I think they owe Australian football fans an explanation.”
He said Visit Victoria hadn't handed over money relating to the match, and only paid for advertising.
Mr Pakula wouldn't be drawn on asserting that Argentina wouldn’t be welcome back to play in Australia, but said authorities would be “pretty wary of a football association that just breaks contract”.
The Argentine federation has not commented on the matter.
Mr Pakula said about 60,000 tickets had already been sold and the promoter has signalled all will be fully refunded.
At the press conference in Rio, Brazil's coach Tite announced his squad for the upcoming friendlies, which includes forward Gabriel Jesus.
The Manchester City player, who was a starter for the national team at the last World Cup, is fighting for a spot in Qatar.
The only new name on the list was Danilo, 21, who plays for Palmeiras.
Brazil will face Serbia, Switzerland and Cameroon in Group G of the World Cup, which starts on November 21.
