Glacier, snow, and ice are the essential components of the Himalayan cryosphere and provide a sustainable water source for different applications. Continuous and accurate monitoring of glaciers allows the forecasting analysis of natural hazards and water resource management. In past literature, different methodologies such as spectral unmixing, object-based detection, and a combination of various spectral indices are commonly utilized for mapping snow, ice, and glaciers. Most of these methods require human intervention in feature extraction, training of the models, and validation procedures, which may create bias in the implementation approaches. In this study, the deep learning classifier based on ENVINet5 (U-Net) architecture is demonstrated in the delineation of glacier boundaries along with snow/ice over the Bara Shigri glacier (Western Himalayas), Himachal Pradesh, India. Glacier monitoring with Landsat data takes the advantage of a long coverage period and finer spectral/spatial resolution with wide coverage on a larger scale. Moreover, deep learning utilizes the semantic segmentation network to extract glacier boundaries. Experimental outcomes confirm the effectiveness of deep learning (overall accuracy, 91.89% and Cohen’s kappa coefficient, 0.8778) compared to the existing artificial neural network (ANN) model (overall accuracy, 88.38% and kappa coefficient, 0.8241) in generating accurate classified maps. This study is vital in the study of the cryosphere, hydrology, agriculture, climatology, and land-use/land-cover analysis.