The disciplinary commission of the French League (LFP) imposed the sanction on Thursday after fans threw a barrage of fireworks outside the Furiani stadium in Corsica on Wednesday as Bastia's 2-1 defeat by Olympique Marseille was played behind closed doors.
"Outraged by the decision, Jo Bonavita, responsible for the logistics at the club, has decided to start a hunger strike this morning in the light of the sanctions imposed by the LFP," the club said on their website.
The 73-year-old Bonavita is a much-loved figure at Bastia, where he has been working since 1981.
The LFP said on Thursday security could not be guaranteed in or around Bastia's stadium for the time being.
The ground was empty for the game against Marseille after violent incidents in the stands marred their match with neighbours Ajaccio in October.
The disciplinary commission is also investigating two other games including the League Cup quarter-final against Lille, which was interrupted for five minutes after a linesman was hit by a missile two weeks ago.
Promoted Bastia, 15th in the league standings, travel to champions Montpellier on Saturday. Their next home game is scheduled for December 22 against strugglers Nancy.
The league said in a statement on Friday that the game would be played in Gueugnon on the mainland.
