Akpan, 25, had a goal disallowed for handball in Tuesday's loss at Sheffield Wednesday, before being shown a red card by Scott Duncan for his protests.
Blackburn have also been charged with failing to ensure players conducted themselves in an orderly fashion.
Akpan and Rovers have until 20 and 21 February respectively to respond.
A three-match ban is the standard punishment for a red card for violent conduct.
However, it is alleged that Akpan's behaviour constituted violent conduct in circumstances where the standard punishment that would otherwise apply is clearly insufficient.
He is currently banned for three matches, including Sunday's FA Cup tie with Manchester United.
In 1998, then-Sheffield Wednesday striker Paolo di Canio was banned for 11 games for pushing referee Paul Alcock to the ground.
Seven years later, Southampton midfielder David Prutton was suspended for 10 matches after admitting two charges of improper conduct, having pushed referee Alan Wiley and attempting to confront another official.
The Football Association has charged Blackburn midfielder Hope Akpan with violent conduct after he was sent off for pushing a referee.