The line-up for Wednesday's quarter-finals will also see two-time winners Spain take on a strong Russian side and another all-Europe tie between Portugal and Italy.
Colombia and Ukraine complete the draw as the indoor football event climaxes after two weeks of fierce competition in Bangkok.
The defending champions, fresh from their 16-0 second round mauling of hapless Panama, are favourites to overcome Argentina, aware victory will hand them a semi-final spot against unfancied Colombia or Ukraine.
Despite his side enjoying a 5-0 record in head-to-head matches, Brazil coach Marcos Sorato predicted a tough game against their neighbours.
"History has nothing to do with it because this game is special," he told FIFA.com website ahead of the game, describing Argentina as "a very competitive side".
Brazil coasted through their qualifying group, winning all three games, scoring 20 and conceding just twice.
That goal tally was bettered by a rampant Russia who found the net 27 times and are yet to concede after four games, making them firm challengers for the title.
But their miserly defensive record is likely to face a stern test when they meet Spain, tournament winners in 2000 and 2004, in a repeat of this year's Futsal Euro final, which the Iberians also won.
"It'll be a very difficult game because Russia have a terrific team," Spain's Fernandao told FIFA.com.
But the Brazilian-born striker fired a warning saying the indoor national team was in Thailand to win, an achievement that would emulate the heroics of the better-known senior team who are both World and European champions.
"We came to Thailand to become world champions. We don't want to lose or draw. Victory is the only thing that counts for us," he said.
Football's governing body FIFA forced Thailand to move the tournament's knockout stages -- including Sunday's final -- from a new $40 million stadium after construction delays meant the venue failed safety tests.