Climate change has had a strong impact on grain production in the Lower Lancang–Mekong River Basin (LMB). Studies have explored the response of LMB rice yield to climate change, but most of them were based on climate projection data before CMIP6 (Coupled Model Intercomparison Project Phase 6). Based on the latest CMIP6 climate projection data and considering three emission scenarios (SSP1-2.6, SSP2-4.5, and SSP5-8.5), this study used the crop growth model (AquaCrop) to simulate and project the LMB rice yield and analyzed the correlation between the yield and the temperature and precipitation during the growth period. The results show that the output of rice yield will increase in the future, with greater yield increases in the SSP5-8.5 scenario (about 35%) than in the SSP2-4.5 (about 15.8%) and SSP1-2.6 (about 9.3%) scenarios. The average temperature of the rice growth period will increase by 1.6 °C, 2.4 °C, and 3.7 °C under the SSP1-2.6, SSP2-4.5, and SSP5-8.5 scenarios, respectively. The rice yield was predicted to have a significant positive response to the increase in temperature in the near future (2021–2060). In the far future (2061–2100), the rice yield will continue this positive response under the high-emission scenario (SSP5-8.5) with increasing temperature, while the rice yield under the low-emission scenario (SSP1-2.6) would be negatively correlated with the temperature. There will be a small increase in precipitation during the rice growth period of LMB in the future, but the impact of the precipitation on the rice yield is not obvious. The correlation between the two is not high, and the impact of the precipitation on the yield is more uncertain. This result is valuable for the management of the rice cultivation and irrigation system in the LMB, and it will help the government to adapt the impact of climate change on the rice production, which may contribute to the food security of the LMB under climate change.