1963–64 Albanian Cup (Albanian: Kupa e Shqipërisë) was the 14th season of Albania's annual cup competition. It began on August 1963 with the First Round and ended on May 1964 with the Final match. KF Tirana were the defending champions, having won their second Albanian Cup last season, but failed to defend the title. The cup was won by KF Partizani. The rounds were played in a one-legged format similar to those of European competitions. If the number of goals was equal, the match was decided by extra time and a penalty shoot-out, if necessary.