The 44-year-old took charge of the Terriers in February 2013, helping them avoid relegation that year and then leading them to a 17th-place finish last term.
However, a 4-0 drubbing at home to Bournemouth on the opening day of the new campaign saw Robins and his players jeered by angry fans.
And following a meeting with Huddersfield's board on Saturday, it was mutually agreed Robins would step aside.
A statement on the club's website read: "Following yesterday's first day defeat, Mark met with the board of directors. At the conclusion of the meeting, Mark and the directors all agreed it would be in the interests of all parties to part company.
"Accordingly, Mark's contract has ended amicably and by mutual consent.
"Huddersfield Town would like to place on record its thanks to Mark and wish him all the best for the future."
Town chairman Dean Hoyle added: "Mark has put his all into the job over the past 16 months and has made a big contribution to the club.
"He arrived at the club at a difficult time and immediately impacted to keep us in the Championship.
"Mark's approach to this has been refreshing. He has always put the club before himself and worked tirelessly on the training ground to change our way of playing and we have seen that come to fruition.
"Mark will be someone that I personally, and we as a club, will always remain in contact with."
Assistant manager Steve Thompson will take charge of the team during Sunday's training session, along with first-team coach Steve Eyre.
- Sports & Recreation
- Huddersfield Town