The Yorkshire club ended Jackson's second spell as Terriers manager after Saturday's 5-1 hammering at Nottingham Forest.
It left them 11 points from the play-off places, with the club's board saying this was not acceptable.
"The board's minimum aim for the season was to achieve a play-off position, but this objective is looking remote," read a statement.
"Peter made a major contribution to the club as it emerged from administration and helped us achieve out early successes.
"We would like to thank Peter most sincerely for his services over the last three-and-a-half years and wish him the best for the future."
Jackson had returned to Huddersfield in June 2003, with the club struggling in what is now League Two and in administration. He had previously bee in charge between 1997 and 1999.
Academy manager Gerry Murphy will take charge of the side against Bradford on Saturday.