Understanding the spatiotemporal characteristics of drought and its impacts on vegetation is a timely prerequisite to ensuring agricultural, environmental, and socioeconomic sustainability in Sri Lanka. We investigated the drought characteristics (duration, severity, frequency, and intensity) from 1990 to 2020 by using the Standardized Precipitation Evapotranspiration Index (SPEI) at various timescales and the cumulative and lagged effects on vegetation between 2000 and 2020 across the climatic zones of Sri Lanka (Dry, Wet, and Intermediate). SPEI indexes at 1-, 3-, 6-, 12-, and 24-month scales were used to analyze the drought characteristics. Frequent droughts (~13%) were common in all zones, with a concentration in the Dry zone during the last decade. Drought occurrences mostly ranged from moderate to severe in all zones, with extreme events more common in the Dry zone. This research used SPEI and the Standardized Normalized Difference Vegetation Index (SNDVI) at 0 to 24-month scales to analyze the cumulative and lagged effects of drought on vegetation. Cumulated drought effects and vegetation had maximum correlation coefficient values concentrated in the −0.41–0.98 range in Sri Lanka. Cumulated drought effects affected 40% of Dry and 16% of Intermediate zone vegetation within 1–4 months. The maximum correlation between the lagged drought effect and vegetation SNDVI showed coefficient values from −0.31–0.94 across all zones, and the high correlation areas were primarily distributed in Dry and Intermediate zones. Over 60% of the Dry and Intermediate zones had a lagged drought impact within 0 to 1 month, while 52% of the Wet zone experienced it over 11 months. The resulting dominant shorter timescale responses indicate a higher sensitivity of vegetation to drought in Sri Lanka. The findings of this study provide important insights into possible spatiotemporal changes of droughts and their possible impact on vegetation across climate zones.