The two sides clash on Monday 29th June (19:00 CEST) in Houston and record five-time champions Brazil will be favourites to reach the next round.
But Japan, considered by some to be outsiders to go far at the tournament in North America, beat Carlo Ancelotti's side 3-2 in a home friendly in October.
And Minamino, who is at the World Cup in a non-playing capacity after suffering a serious knee injury, said they can pull off another surprise.
"If we play with the underdog mentality, as we always have, I believe we have the ability to make something happen in these one-off games," said the 31-year-old, who scored in the friendly win eight months ago.
Speaking to reporters on Friday at Japan's training base near Nashville, Tennessee, Minamino said attacker Takefusa Kubo could play a part after a knee injury.
The Real Sociedad winger came off in the 2-2 draw with the Netherlands that launched Japan's World Cup campaign, and was not fit to feature in the subsequent Group F games against Tunisia and Sweden that ultimately saw Japan secure second place.
"He is especially spirited, so he needs no encouragement from me," Minamino said, according to Kyodo News.
"Everyone believes we will welcome him back in the knockout stage, and he is rehabbing with that same belief."
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