The 37-year-old German managed just one victory from his 19 games in charge, following Town's 2-1 home defeat to Fulham on Friday night.
And Hodgkinson said: “Last night’s decision was not one that I, nor the Board, took lightly, but I believe it is one that had to be made,” the Chairman explained to htafc.com.
“Jan walked into a very difficult situation in January; something that we were all aware, and mindful, of. However, I have seen no evidence of the impact on our performances that I was expecting following a full pre-season.
“Jan is a fantastic man and he’s worked tirelessly for this Club during his time here, but unfortunately it has not worked. I believe he is a good coach and I sincerely hope he will be successful in the future.
“I believe our players are better than we have seen so far this season. We will work to appoint a new Head Coach who can get the best from them and bring an identity back to our performances.”
Siewert took over in January after David Wagner left the club, but could not prevent their relegation from the Premier League.
His only win was a 1-0 victory over Wolves in his fifth game at the helm as Huddersfield finished bottom, relegated by March.
First team coach Mark Hudson will take temporary charge of the team, beginning with the Sky Bet Championship game at Cardiff City on Wednesday.