The 'Godfather'-style gift was found in a box along with a message addressed to former club president Massimo Ferrero (71) and current vice-president Antonio Romei (58) reading "the next heads will be yours", a spokesman for the club said.
The police have been notified, he added.
Ferrero, who still controls Sampdoria via a family holding, resigned from his position after he was arrested in 2021 on financial charges unrelated to football.
He has angered fans who say he is running down Sampdoria's finances and refusing to sell the club to new owners capable of rescuing it from financial and sporting disaster.
The Genoa-based side currently sit second-bottom of the table on 11 points after 23 games, eight points adrift of safety. They next travel to fifth-placed Lazio on Monday.
Last month, a blank bullet was delivered to Sampdoria's headquarters accompanied by threats against Ferrero and Edoardo Garrone, a previous owner of the club.
In a statement: Sampdoria responded: "Any kind of attack on a member of the board of directors represents an attack on all its members, on their work and on the seriousness and abnegation with which they have approached this important task.
"Since its appointment, the board has operated in cohesion, unity of purpose and independence with the sole purpose of ensuring the continuation of Sampdoria's business and sporting activities pending the transition to new ownership.
"It is precisely in this direction that the professionalism and preparation of the vice-president Antonio Romei, with whom the Board hopes to continue to share this delicate phase in the life of the club, will be fundamental."
Other Italian teams have faced similar intimidation in the past.