"I remind every employee, whatever his status within the club, that they are bound by professional secrecy. Therefore, a financial sanction has been imposed on the sports director," Vincent Labrune said in a statement on the club's website.
Deschamps and Anigo have disagreed over control of the club's recruitment policy, local media have reported.
"I will not speak about things that I know of, that you know of and that many people know of," Deschamps told a news last Friday before Marseille's 2-0 victory over AC Ajaccio.
Anigo felt the remark was directed at him.
"He [Deschamps] should think twice before speaking instead of saying stupid things like this," Anigo told reporters on Saturday. "It is irresponsible."
Marseille have made a mediocre start to the season, wining only twice in 11 games. They lie 12th in the Ligue 1 standings, 14 points behind leaders Paris Saint-Germain.
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