The Egypt forward scored the goal that secured his country a place at this year's World Cup, while he has been in superb form since signing for the Reds.
Salah has scored 23 goals for Liverpool already this season following his summer move from Roma.
Club team-mate and Senegal international Sadio Mane came second, with Gabon's Pierre-Emerick Aubameyang third, the Confederation of African Football announced at its gala dinner on Thursday night.
Liverpool boss Jurgen Klopp allowed his two shortlisted players to attend the ceremony in Ghana despite his side playing Everton in the FA Cup on Friday.
Salah will miss the game through a groin injury, but Mane could well play.