According to the Sydney Morning Herald, Drogba, who plays for Turkish giants Galatasaray, removed his club shirt after a match Friday against SB Elazigspor to reveal a T-shirt that read "Thank You Madiba".
His teammate Eboue also honoured the South African anti-apartheid hero, who died aged 95 on Thursday, with a T-shirt that said "Rest in Peace Nelson Mandela".
The federation said the two players faced disciplinary action for breaching a ban on wearing political slogans and messages on T-shirts.
Image: Didier Drogba
Photograph: BT Sports Panel on Twitter