The Championship duo were charged with failing to control their players during the latter stages of Burton's surprise 1-0 win at the John Smith's Stadium on April 1.
Burton have been fined £5,000 by English football's governing body, while Huddersfield have been hit with a £12,500 fine due to it being their second such offence within 12 months.
"Burton Albion and Huddersfield Town have been fined £5,000 and £12,500 respectively following their Championship fixture on 1 April 2017," read a statement from the FA.
"Both clubs admitted an FA charge of failing to ensure their players conducted themselves in an orderly fashion in or around the 88th minute of the match.
"Burton Albion received the standard penalty for the breach. However, as this was Huddersfield Town's second breach of Rule E20 in a 12-month period, following a similar incident during their fixture against Leeds United on 5 February 2017, the case was considered to be 'non-standard'."
Huddersfield's next match sees them host Fulham on Saturday, while Burton take on Leeds United.