Drought, a recurring natural phenomenon in South Asia's monsoon climate, presents challenges in delineating its spatiotemporal patterns within complex topographies. This study investigated the impact of the orographic barrier in the rice‐dominated agricultural region of northeastern India and Bangladesh on drought characteristics during 1951–2020, employing the relative Standardized Precipitation Index (rSPI) and relative Standardized Precipitation‐Evapotranspiration Index (rSPEI) across 3‐, 6‐ and 12‐month scales. The results indicate that even in the rainiest region of the world, droughts extend beyond the limits of the dry season inherent in the monsoon regime. These mostly regional droughts exhibit weak correlations with the core of the Indian subcontinent and other parts of Bangladesh. The region's orographic barrier has a greater influence on drought intensity than on frequency. The rSPI index, which depends solely on rainfall, may overestimate drought intensity and frequency in regions with high seasonal/annual rainfall and substantial intermonthly variability. In contrast, the rSPEI index, which depends on both rainfall and potential evapotranspiration (PET), better reflects the spatial variation of drought in complex terrain, identifying the leeward hinterland of the orographic barrier as the most drought‐prone area. The two indices give similar results for drought characteristics away from the barrier. Furthermore, the orographic barrier exerts a negligible influence on the trends in rSPI and rSPEI. Principal component analysis (PCA) highlights the influences of the rainfall coefficient of variation and elevation on rSPI, while the PET coefficient of variation strongly influences rSPEI. Strategies to minimize the adverse effects of drought in complex topography and year‐round cropping should be local and season‐specific. These include using shorter‐growing, drought‐resistant rice varieties and adjusting planting schedules in rain shadow areas during the summer monsoon. These efforts should be complemented by integrating indigenous irrigation methods with modern practices such as roof water harvesting and tube wells in winter.