The southern Italy club’s captain Paolo Cannavaro and fellow defender Gianluca Grava were banned for six months for “failing to report evidence of corruption”, the federation added.
Napoli, Cannavaro and Grava — on their part — have issued a formal denial of wrongdoing.
The club has also complained about the timing of the punishment, which they are expected to appeal through the FIGC’s justice court.
A statement on sscnapoli.it read: “The president Aurelio de Laurentiis, the head coach Walter Mazzarri and the whole team are calm, being confident that no violation could be attributed to Napoli.”
Napoli were in third spot before the ruling but now fall to fifth, 10 points behind defending champions and league leaders Juventus, in a severe blow to their title hopes.
The FIGC disciplinary committee also said it had suspended former goalkeeper Matteo Gianello for three years and three months for his involvement in an attempt to fix the match between Napoli and Sampdoria on May 16, 2010.
The sport authority hearing is separate from a wider criminal investigation into suspect matches headed by prosecutors in three Italian cities that has implicated players from the top flight and second-tier Serie B.
This season, Serie A sides Sienna have been docked six points, Atalanta two and Torino one as a result of the illegal betting investigation.
Photos: Kareena Kapoor Khan, Kangana Ranaut at the Mumbai airport
Photos: Virat Kohli-MS Dhoni's bromance, Team India in LOL mode
Bollywood celebs show you colours for Navratri 2017
Birthday special: Chris Gayle and his multiple records in cricket
In Pictures: 17 dreaded on-screen villains of Bollywood