The AIA's vice president Narciso Pisacreta and referee selector Nicola Rizzoli have also been recipients of sinister deliveries.
The threats have arrived at the AIA following protests surrounding the use of VAR (video assistant referees) in Serie A. The technology has had mixed results this season.
Last month, hundreds of Lazio fans showed up outside the Italian football federation's offices in Rome to protest VAR.
As well as informing the press about the latest development, Nicchi has condemned a journalist who suggested that fans "should shoot the referees" and says the police and Italy's Interior Ministry are investigating the packages and their origins.
VAR will be used at the 2018 Russia World Cup.
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