Fiorentina had said on Monday that Barone remained in hospital on life support after collapsing on Sunday as the team were leaving the hotel for their Serie A match at Atalanta, which was postponed.
"It is with deep sorrow and immense sadness that Fiorentina confirms the loss of one of its figureheads, a person who has marked the recent history of the club and who will never be forgotten," the club said in a statement.
"General Director Giuseppe Barone passed away today at the San Raffaele Hospital in Milan after suddenly falling ill on Sunday," it said.
"He was a treasured friend who always stayed strong in the happiest and, above all, the most difficult moments."
Barone, who would have turned 58 on Wednesday, took up his role at Fiorentina in November 2019.
