1991–92 Albanian Cup (Albanian: Kupa e Shqipërisë) was the fortieth season of Albania's annual cup competition. It began on August 1991 with the First Round and ended on May 1992 with the Final match. The winners of the competition qualified for the 1992-93 first round of the UEFA Cup. KF Partizani were the defending champions, having won their twelfth Albanian Cup last season. The cup was won by KS Elbasani.
The first round was played in a single round-robin matches within 8 qualifying groups. The other 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 shootout, if necessary.