Tigers captain Ian Ashbee and Charlton's Lloyd Sam were red carded following the incident, which took place shortly before the break at the KC Stadium.
The incident was triggered by Ashbee's challenge on Sam, with both sides now set to face a charge of failing to control their players.
"We will be considering the referee's report and investigating the incident," said an FA spokesman.
"We will also be looking at video evidence before deciding what further action is necessary."