The 54-year-old Frenchman departed after Saturday's 0-1 home defeat by Al Ahli of Egypt that confirmed Esperance's exit from the African Confederation Cup.
Anigo had only joined Esperance in late June and lost five of his seven games in charge.
His assistant Bernard Rodriguez, who joined with Anigo, is to take over, club officials said.
(Reporting by Mark Gleeson, editing by Amlan Chakraborty)
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