1965–66 Albanian Cup

1965–66 Albanian Cup (Albanian: Kupa e Shqipërisë) was the sixteenth season of Albania's annual cup competition. It began in August 1965 with the First Round and ended in May 1966 with the Final matches. Vllaznia were the defending champions, having won their first Albanian Cup last season. The cup was won by Partizani.

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.