Yield optimization of young Japanese ‘Nanko’ apricot (Prunus mume Siebold et Zucc.) trees requires adequate and timely irrigation. Here, different irrigation amounts (5, 10, 15, and 20 mm) were applied to three-year-old trees from July (initiation of flower bud differentiation stage) to March (fruit setting stage), when the pF meter reading was 2.7. Then, the effects on flower buds and fruit setting rate were assessed. Trees supplied with the 5 and 10 mm irrigation amounts experienced severe drought stress. Limited water supply reduced flower-bud growth and flower-bud number, possibly caused by several factors including inhibition of flower-bud differentiation in summer and abscission of immature buds just before anthesis. Limited irrigation did not inhibit complete flower formation, except under the 5 mm irrigation treatment, but flower size and fruit-setting rate were negatively affected. These findings indicated that insufficient irrigation caused poor flower formation and low fertility. Combined, these effects explained the observed yield reduction and all irrigation treatments, except for the 20 mm one, severely affected productivity. Based on these results, we recommend that the amount of water applied to young Japanese apricot trees from flower-bud differentiation to fruit set should be no less than 20 mm to achieve adequate flower bud growth and a high fruit-setting rate for high fruit yield.