Maldini, who also managed AC Milan, died at the weekend, the club announced on Sunday.
Addio caro Cesare. Oggi il mondo piange un grande uomo e noi parte della nostra storia. Ci mancherai. pic.twitter.com/vUBSqNI6pU— AC Milan (@acmilan) April 3, 2016
A minute of silence was held in his honour before every league game in Italy on Sunday.
Maldini became Italy coach in 1996, going on to lead the team into the 1998 World Cup in France, where they lost to their hosts in the quarter-finals on penalties.
As a player, he won four Series A titles with AC Milan and was captain in 1963, when the team became the first Italian side to win the European Cup. He then managed the club between 1972 and 1974.
He went on to coach Paraguay for the World Cup in 2002 but the side didn't go beyond the group stage, and so he returned to Italy to work as a scout for AC Milan.
Maldini was born in Trieste in 1932. He started his career with Triestina in 1952, before transferring to AC Milan in 1954.
One of his six sons, Paolo, also played for Italy and AC Milan.