Soft scald and soggy breakdown are important postharvest physiological disorders of apple (Malus × domestica). ‘Honeycrisp’ and some of its offspring are particularly susceptible to developing these disorders. The purpose of this study was to identify molecular markers associated with high incidences of soft scald and soggy breakdown for use in marker-assisted breeding. Towards this aim, we employed a pedigree-based approach using mostly germplasm related to ‘Honeycrisp.’ Two quantitative trait loci (QTL) were consistently identified on linkage groups (LGs) 2 and 16 across the 2014 and 2015 harvest years. The same QTL were identified for both storage disorders, indicating that they may be physiologically related. ‘Honeycrisp’ is homozygous for an identical by state haplotype at the LG2 QTL that was consistently associated with a deleterious effect on soft scald and soggy breakdown incidence. This haplotype was traced through SNP-confirmed pedigrees to the following cultivars: ‘Grimes Golden,’ ‘Northern Spy,’ ‘Rome Beauty,’ and ‘Fireside’ and is common in derived apple germplasm. Haplotypes at the LG16 QTL could not be adequately characterized due to variation between years combined with effects of this QTL being of relatively smaller size and being most evident in individuals that carry two copies of the deleterious haplotype at the LG2 QTL. These results suggest that limiting homozygosity of the deleterious haplotype at the LG2 QTL through marker-assisted breeding would be a valid strategy to limit soft scald and soggy breakdown incidences in apple seedling populations.