The Fire missed out on a post-season spot in the Eastern Conference by just goal difference to Montreal Impact.
Chicago were beaten 5-2 by New York Red Bulls in their final regular-season game on Sunday, failing to take advantage of Montreal's 1-0 loss to Canadian rivals Toronto a day earlier.
Klopas had held his position since 2011 and also finished agonisingly short of a play-off spot in his first season.
"No one appreciates Frank's passion, integrity and competitive spirit more than me," said franchise owner Andrew Hauptman.
"Frank has been a big part of this organization for many years as a player, technical director and coach. I want to personally thank him for his efforts over this period. He is a wonderful friend and will always be a member of the Fire family.
"There have been many highlights over these years but I think now is an appropriate time to make a transition to new leadership.
"Of course, making this team compete for championships on a consistent basis is our first priority."
Klopas is already the second head coach to depart a franchise after the regular season, with Schellas Hyndman having resigned from Dallas on Saturday after their 2-1 loss at San Jose Earthquakes.
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