Amrani stepped down on Sunday, just over a week after elections swept long-standing president Issa Hayatou from power.
El Amrani, in a letter to African football associations, said he would be departing on Monday, but gave no reason for his decision.
The 37-year-old Moroccan had served as secretary general for the last six years.
Hayatou was deposed as Caf president at elections in Ethiopia, where six of his allies on the body’s executive committee also lost their positions.
New Caf president Ahmad is due to meet staff members in Cairo on Monday.