Following Saturday's 4-0 home defeat against Bournemouth, Robins, 44, met with the board and it was agreed he would leave his post.
A club statement read: "Mark and the directors all agreed it would be in the interests of all parties to part company."
Former Coventry boss Robins took over from Simon Grayson in February 2013.
He helped the Terriers avoid relegation in his first season and guided the club to a 17th-place finish last term.
However, the club won just two of their last 13 league games in a 2013-14 campaign that finished with a total of 23 defeats.
Following Saturday's loss at the John Smith's Stadium, the former Rotherham and Barnsley boss was jeered by the fans.
Huddersfield chairman Dean Hoyle commented: "Mark has put his all into the job over the past 16 months and has made a big contribution to the club."
Assistant manager Steve Thompson will take charge of the team during Sunday's training session, along with first-team coach Steve Eyre.
Thompson, 49, joined Huddersfield from Blackpool in June this year and Eyre was promoted the same month following a shake-up of Robins' backroom staff in May.
Huddersfield Town have parted company with manager Mark Robins after just one game of the Championship season.