In this study, we analyzed the predictions of hydrological droughts in the Lam Chiang Kri Watershed (LCKW) by using the Soil and Water Assessment Tool (SWAT) and streamflow data for 2010–2021. The objective was to assess the streamflow drought index (SDI) for 5-, 10-, 25-, and 50-year return periods (RPs) in 2029 and 2039 in two representative concentration pathway (RCP) scenarios: the moderate climate change scenario (RCP 4.5) and the high-emission scenario (RCP 8.5). The SWAT model showed high accuracy (R2 = 0.82, NSE = 0.78). In RCP4.5, streamflow is projected to increase by 34.74% for 2029 and 18.74% for 2039, while in RCP8.5, a 37.06% decrease is expected for 2029 and 55.84% for 2039. A historical analysis indicated that there were frequent short-term droughts according to SDI-3 (3-month-period index), particularly from 2014 to 2015 and 2020 to 2021, and severe droughts according to SDI-6 (6-month-period index) in 2015 and 2020. The RCP8.5 projections indicate worsening drought conditions, with critical periods from April to June. A wavelet analysis showed that there is a significant risk of severe hydrological drought in the LCKW. Drought characteristic analysis indicated that high-intensity events occur with low frequency in the 50-year RP. Conversely, high-frequency droughts with lower intensity are observed in RPs of less than 50 years. The results of this study highlight an increase in severe drought risk in high emission scenarios, emphasizing the need for water management.