The 30-year-old scored the opener at Stamford Bridge but faces a three-match ban for hurling the missile, thought to be a coin, towards the stands during his celebrations.
An FA regulatory commission will hear the case on Tuesday and make their final decision based on video evidence and written submissions.
Drogba was substituted later in the game, just ahead of Burnley equalising, before they went on to record a victory on penalties.
It was Drogba's first goal of an injury-hit season, and he is now expected to spend more time on the sidelines.
The Ivory Coast international has struggled with a knee injury, limiting him to five Barclays Premier League appearances this season, with Nicolas Anelka leading Luiz Felipe Scolari's attack in his absence.
The former Marseille striker issued an apology for the incident immediately after the Burnley defeat.