He started his youth career in Drøbak-Frogn IL and represented Norway as a youth international.[1][2] Ahead of the 1980 season he joined Moss FK,[3] and already in 1981 he went on to a second-choice spot in Vålerenga IF.[4] Ahead of the 1983 season he signed for Hamarkameratene, but as the clubs never agreed on the prize, the prize was set by a Football Association tribunal. Hamarkameratene refused to pay this prize as well, and Moe re-signed for Vålerenga just as the season started.[5][6] In 1984 he joined Strømsgodset IF,[7] played university soccer at Boston University, and rejoined Drøbak-Frogn in 1986.[8]
From 1988 to 1990 he played for SFK Lyn. He then retired, and only played one post-retirement match, in the 1993 Eliteserien.[9]