The former double European Cup winners are struggling in England's second-tier and were recently the subject of a takeover attempt by a U.S.-owned consortium.
Forest have taken two points from their last 21 and Saturday's 0-0 draw with Birmingham City left them 20th, three points above the relegation zone.
The 52-year-old Montanier, who has also been in charge at Stade Rennes, Real Sociedad, Valenciennes and Boulogne, is the seventh permanent manager to leave Forest since the club was taken over by businessman Fawaz Al Hasawi in July 2012.
Forest have put academy manager Gary Brazil in charge until a successor is named.
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(Reporting by Neil Robinson; Editing by Ken Ferris)
