In the context of global warming, the strength and frequency of drought events are projected to grow in the future, and the onset of drought can have dramatic effects on vegetation growth in terrestrial ecosystems. Central Asia is the largest non-territorial drought area in the world, and the response of vegetation to drought events is extremely sensitive in the area. However, few studies have quantified and compared the vegetation gross primary productivity (GPP) response to the lagged and cumulative effects of drought. In this research, the solar-induced chlorophyll fluorescence GPP and Standardized Precipitation Evaporation Index (SPEI) were used to analyze the time and space patterns of vegetation GPP and the SPEI in Central Asia and to quantify and compare the lagged and cumulative effects of drought on the GPP of various vegetation types. During the period from 2000 to 2018, the general trends of vegetation GPP showed a slight increase in Central Asia, with the ratio of variation being 1.35 g C m−2 y−1 and a spatially decreasing distribution from north to south. SPEI showed a trend of decreasing and then increasing over a period of 19 years, with a slight decreasing (drying) trend and a rate of change of −0.02 y−1, and the overall spatial pattern was drying out from north to south. In 13 months, 72.44% of regional droughts had lagged impacts on vegetation. The maximum correlation coefficients of vegetation and the lagged effectiveness of drought were concentrated in the range of 0.15–0.35, and the high correlation was distributed in southern and northwestern Kazakhstan, which are prairie regions. Of the regions in Central Asia, 75.86% showed cumulative drought effects concentrated at 9–12 months. The maximum correlation coefficients were concentrated in the range of 0.20–0.50, and the high correlation regions were primarily situated in south Kazakhstan and east Uzbekistan. Comparing the correlation coefficients of the lagged effect of vegetation GPP and SPEI with the cumulative effect shows that the cumulative rather than lagged impacts of drought on vegetation cover were found in 86.75% of the regions in Central Asia. This research enhances our comprehension of the influence of drought events on ecosystems in arid regions and has a certain reference value for helping arid region ecosystems to cope with global climate change.