Rice false smut (RFS) is a late-onset fungal disease that primarily affects rice panicle in recent years. Severe RFS can decrease the yield by 20–30% and severely affect rice quality. This research used hyperspectral remote sensing data from unmanned aerial vehicles (UAV). On the basis of genetic algorithm combined with partial least squares to select the feature bands, this paper creates a new method to use the Pearson correlation coefficient method and Instability Index between Classes (ISIC) method to further select characteristic bands, which further eliminated 27.78% of the feature bands when the model monitoring accuracy was improved overall. The prediction accuracy of the Gradient Boosting Decision Tree model and Random Forest model was the best, which were 85.62% and 84.10%, respectively, and the monitoring accuracy was improved by 2.22% and 2.4% compared with that before optimization. Then, based on the UAV hyperspectral data and the combination of characteristic bands selected by the three band optimization methods, the sensitive band ranges of rice false smut monitoring were determined, which were 698–800 nm and 974–997 nm. This paper provides an effective method of selecting characteristic bands of hyperspectral data and a method of monitoring crop diseases’ using unmanned aerial vehicles.