The Palermo Civico hospital said in a statement that Schillacci died on Wednesday morning after being admitted 11 days ago.
Schillaci scored six goals for Italy during the 1990 World Cup. He came on as a substitute during Italy's opener against Austria, scored in a 1-0 victory, and went on to earn the Golden Boot awarded to the tournament's top scorer. He only scored one other goal for Italy in his career.
Italian soccer federation president Gabriele Gravina announced that a minute of silence would be held in memory of Schillaci before all games in the country for the rest of the week.
"The uncontrollable celebrations, in which his face was the symbol of shared joy, will remain forever part of Italian soccer (history)," Gravina said. "Totò was a great player, a symbol of tenacious desire and redemption. ... His soccer was full of passion. And that fearless spirit made everyone appreciate him and will make him immortal."
Schillaci also won the Golden Ball award at the 1990 World Cup as the tournament's top player ahead of Lothar Matthaus and Diego Maradona.
Schillaci played for Messina, Juventus, Inter Milan and Japanese team Jubilo Iwata during his club career.
"Ciao Totò," Juventus said on Instagram.
"You made an entire nation dream during the Magical Nights of Italia '90," Inter said on its social media channels.
West Germany won the 1990 World Cup, beating Argentina in the final, while Italy beat England for third place with a winning penalty kick from Schillaci.
Roberto Baggio, who scored Italy's opening goal in the third-place match, wrote on Instagram, "Ciao my dear friend."
Having been born and raised in Palermo, the Palermo soccer team announced that it would hold a public viewing of Schillaci at its Renzo Barbera stadium ahead of the funeral, the Gazzetta dello Sport reported.