Udinese's game at Torino, Fiorentina's visit to Cagliari, Genoa's match against Lazio and Juventus' trip to Parma will be rescheduled.
The games will have to fit into a congested finish to the season, potentially clashing with the Champions League semi-finals.
Serie A also postponed matches in its youth league.
The Italian football federation (FIGC) announced that all games across professional and amateur football on Monday would be rescheduled to a later date.
The FIGC hailed the Pope as "an example of Christian charity and dignity in suffering, always close to the world of football."
The Vatican said Pope Francis, a keen football fan, died aged 88 on Monday.
