This paper utilizes the data on crop drought affected area rate and crop drought disaster area rate in Henan Province from 1978 to 2020 to explore the evolution patterns of agricultural drought disasters in the region. The Mann–Kendall test was employed to identify the trend and mutation characteristics of the disaster situation, while the Morlet wavelet method was applied to analyze its periodicity. A grey dynamic multivariable catastrophe prediction model was proposed to forecast the potential years for future agricultural drought disasters in Henan Province. The results indicate: (1) Over the past 42 years, both the crop drought affected area rate and crop drought disaster area rate in Henan Province have exhibited a significant downward trend. (2) No mutation was observed in the crop drought affected area rate during the study period, whereas a mutation in the rate of crop drought disaster area occurred in 2008. (3) Both the crop drought affected area rate and crop drought disaster area rate displayed multi-timescale periodic changes. (4) The potential years for agricultural drought disasters in the next decade are predicted to be 2024 and 2029, respectively. The findings of this study offer a scientific foundation for the development of medium to long-term management strategies for agricultural drought disaster mitigation in Henan Province.