1963–64 Albanian Cup (Albanian: Kupa e Shqipërisë) was the 14th season of Albania's annual cup competition.
It began in August 1963 with the First Round and ended in May 1964 with the Final match.
17 Nëntori were the defending champions, having won their second Albanian Cup last season, but failed to defend the title.
[1] 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.