1972–73 Albanian Cup (Albanian: Kupa e Shqipërisë) was the twenty-first season of Albania's annual cup competition. It began on August 1972 with the First Round and ended on May 1973 with the Final match. The winners of the competition qualified for the 1973-74 first round of the UEFA Cup. KS Vllaznia were the defending champions, having won their second Albanian Cup last season. The cup was won by KF 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.