Centre back Gallas was scheduled to appear before the media alongside goalkeeper Hugo Lloris at France's base in Knysna, Western Cape, on Tuesday but only Lloris turned up.
"William has decided not to speak to the media for the duration of the World Cup finals," a team spokesman said without elaborating.
Under FIFA rules, teams are obliged to make only one player available to media each day, the spokesman added.
The France team have been under heavy fire from their local media for years and both the players and coach Raymond Domenech have been persistently criticised for the way they communicate.
When Domenech was surprisingly left in charge after his side's Euro 2008 flop, French Football Federation (FFF) president Jean-Pierre Escalettes said both the coach and the players should make an effort with the press.
The players, Escalettes then told a news conference, would need to speak to the media or face sanctions.
French media have suggested Gallas was upset about the fact that the new team captain was fellow defender Patrice Evra, and not himself.
France Football magazine reported on Tuesday that the Arsenal player had received an offer from Greek side Panathinaikos. The fact that he did not want to discuss that news could also partly explain Gallas's decision.
France start their campaign by playing Uruguay on Friday in Cape Town. They will also face Mexico and hosts South Africa in Group A.
