Amrouche was announced as Lybia national team manager in May 2018 and only oversaw one game at the helm.
In his only game in charge, he managed to grab a point the AFCON qualifiers after the goalless stalemate with Bafana in Durban last month.
Reports in Libya suggest Amrouche became disillusioned with his role after not being paid for the last six months, while Libya Observer claims the squad were left confused by his 'random' tactics.
The news comes as a major blow for the African minnows who lead Group E by goal-difference, as they remain level on four points with South Africa.
The Belgian-Algerian managed several other African national teams such as Kenya, Burundi and Equatorial Guinea as well as Algerian giants USM Agler.
Omar Al-Miryami is likely to lead The Middeteranen Knights for the home and away matches against the Super Eagles this week.