1984–85 Albanian Cup (Albanian: Kupa e Shqipërisë) was the thirty-third season of Albania's annual cup competition. It began on August 1984 with the First Round and ended on May 1985 with the Final match. The winners of the competition qualified for the 1985-86 first round of the UEFA Europa League. KF Tirana were the defending champions, having won their sixth Albanian Cup last season. The cup was won by KS Flamurtari.
The rounds were played in a two-legged format similar to those of European competitions. If the aggregated score was tied after both games, the team with the higher number of away goals advanced. If the number of away goals was equal in both games, the match was decided by extra time and a penalty shootout, if necessary.