Monaco said in a statement on Saturday that Kovac was informed of the decision on Thursday during a meeting, adding that reserve team coach Stephane Nado will take over in an interim role for Sunday's French Cup game at second-tier Quevilly-Rouen.
French sports daily L'Equipe reported that Club Brugge coach Philippe Clement will become the new permanent coach.
Clement played 333 games, and scored 45 goals, as a defender for Club Brugge before taking charge in June 2019 and winning two Belgian league titles to make it three in a row, after winning with Genk the previous season.
Although Monaco has won three of its past four league games, a poor start to the season and a failure to qualify for the Champions League via the August playoffs have cost Kovac.
The 50-year-old Kovac's side lost 3-2 on aggregate to Shakhtar Donetsk, despite leading the second leg 2-0 at halftime in Ukraine.
Monaco is four points adrift of second-place Nice and third-place Marseille in the Champions League spots for next season.
Kovac also made a slow start with Monaco last season but then transformed the side's fortunes to finish third behind Paris Saint-Germain and champion Lille.
Monaco started badly this season with one win from six league games — and that was against promoted side Troyes.
Monaco hired Kovac after firing Roberto Moreno in June 2020, citing the former Croatia midfielder's success while coaching Bayern Munich, Eintracht Frankfurt and his own national team.
Although he led Bayern to a league and cup double in 2019, he was fired in November of that year.
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