Akpan was shown a red card for pushing the official in the closing stages of the match last Tuesday having seen a late equaliser controversially disallowed for handball.
The dismissal earned the 25-year-old an automatic three-game ban, and the Football Association has extended that by an additional match after finding the player guilty of violent conduct.
Blackburn have also been fined £5,000 for failing to control their players during the same incident.
"Blackburn Rovers player Hope Akpan will serve a four-match suspension with immediate effect following the game against Sheffield Wednesday on 14 February 2017," read a statement from the FA.
"It was alleged his behaviour in or around the 87th minute of the game constituted violent conduct in circumstances where the standard punishment of three matches would be clearly insufficient. He denied the charge, however, it was found proven following an Independent Regulatory Commission hearing.
"An additional one match suspension was added to the standard punishment the player is already serving following his dismissal. In relation to the same game, Blackburn have been fined £5,000 after the club admitted a charge of failing to ensure its players conducted themselves in an orderly fashion in the 87th minute and accepted the standard penalty."
Akpan has already served one match of the ban but will now miss Blackburn's Championship meetings with Burton Albion, Derby County and Wigan Athletic.