His decision was confirmed on the country's official government website on Thursday although no reason was given.
The much-travelled former France captain announced his intention to leave after a meeting with the FA on Monday .
His departure comes less than a week after Equatorial Guinea, ranked 155th in the world, earned a creditable 1-1 draw with Cameroon in a friendly in Malabo, where the Nations Cup finals kick off on January 21.
Equatorial Guinea are co-hosting the three-week tournament with Gabon.
Radio France International said Michel had given up in frustration over conditions in the former Spanish colony.
Equatorial Guinea, which is rich in oil resources, has a recent history of offering players from Brazil and other countries passports to play for the national team without satisfying the necessary FIFA qualifying criteria.
Michel was hired last December on a 13-month contract.
His move to Malabo continued a nomadic career for one of French football's greats who has coached in 10 different countries.
Michel managed France, Cameroon, Morocco and the Ivory Coast at four World Cup finals and has also worked at clubs in Egypt, Morocco, Qatar, South Africa and the United Arab Emirates.
