The Bayern Munich winger was ruled out of the tournament with a back problem, but was offered the treatment by national team doctor Kevin Le Gall.
His refusal prompted Le Gall to question the German club's medical approach and claim Ribery was scared of needles.
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"Franck belongs to a club whose method of treatment for all ailments, whatever they might be, is based on injections," he said earlier this week.
But Ribery, 31, has now hit back and suggested he was unhappy at being offered the jab, which increases mobility and is used to reduce pain in the affected area.
"I'm not afraid of injections, but I did not want to have a cortisone injection from the French doctor. I know that's not good," he told SID.
In his absence, France opted to call up Southampton midfielder Morgan Schneiderlin, with Didier Deschamps' men kicking off their World Cup campaign against Honduras on Sunday night.