1961 Albanian Cup (Albanian: Kupa e Shqipërisë) was the twelfth season of Albania's annual cup competition. It began on Spring 1961 with the First Round and ended on May 1961 with the Final matches. Dinamo Tirana were the defending champions, having won their sixth Albanian Cup last season.
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.