Categorical scores for disease susceptibility or resistance often are recorded in plant breeding. The aim of this study was to introduce genomic models for analyzing ordinal characters and to assess the predictive ability of genomic predictions for ordered categorical phenotypes using a threshold model counterpart of the Genomic Best Linear Unbiased Predictor (i.e., TGBLUP). The threshold model was used to relate a hypothetical underlying scale to the outward categorical response. We present an empirical application where a total of nine models, five without interaction and four with genomic × environment interaction (G×E) and genomic additive × additive × environment interaction (G×G×E), were used. We assessed the proposed models using data consisting of 278 maize lines genotyped with 46,347 single-nucleotide polymorphisms and evaluated for disease resistance [with ordinal scores from 1 (no disease) to 5 (complete infection)] in three environments (Colombia, Zimbabwe, and Mexico). Models with G×E captured a sizeable proportion of the total variability, which indicates the importance of introducing interaction to improve prediction accuracy. Relative to models based on main effects only, the models that included G×E achieved 9–14% gains in prediction accuracy; adding additive × additive interactions did not increase prediction accuracy consistently across locations.