Amrouche has resigned just days before his side faces Nigeria in an African Nations Cup qualifier. The match is billed for Uyo, Akwa Ibom state.
His departure has been confirmed by the Libyan Football Federation and on Wednesday by Belgian Amrouche, who told the media that he was frustrated by working conditions with the team.
The 50-year-old, who was born in Algeria, was only appointed in May and his first match in charge last month saw Libya force a 0-0 draw in South Africa.
They were forced to play all their home qualifiers at a neutral venue because of the tenuous security situation in the North African country.
Libya travels to face Nigeria on Friday and then play them again in the return in Sfax, Tunisia on Monday.
Libya has four points from their first two games in their bid to qualify for the 2019 finals in Cameroon, ahead of South Africa on goal difference with Nigeria one point behind.
Seychelles are last in the group without any points.