Mt. Munkhkhairkhan is the most crucial region for understanding climate and glaciation changes in Mongolia. This study investigated the relationship between glacial area changes and the climate elements of Mt. Munkhkhairkhan in the Mongolian-Altai Mountains using a remote sensing approach, in-situ observations, the Mann–Kendall (MK) test, Innovative Trend Analysis Method (ITAM), Sen’s slope estimator test, and statistical analysis. The study results showed that for the last 30 years, the annual average air temperature of Mt. Munkhkhairkhan has been slightly increasing. Total annual precipitation (mainly snow) in the mountain area decreased from 1990 to 2000, but since 2000, a significant increase in precipitation levels has appeared. For the last 30 years, the glacial area has decreased by 32% to 11.7 km2. Multiple regression results showed a strong correlation between Temperature, Precipitation, and Glaciers (Multiple R = 0.69, R2 = 0.48). Ruther indicated that Temperature (t = −2.332, p = 0.036) and Precipitation (t = −3.212, p = 0.007) were significant predictors in the model. Air temperature and precipitation explained 48 percent of the change in the glacier area, and R = 0.69 is a strong correlation. The glaciers and snow area in the study area have changed due to climate warming and precipitation changes and are located in arid and semi-arid regions of Central Asia. This study of Mt. Munkhairkhan shows that climate change significantly impacts glaciers and snow.