Methane (CH4) is a major greenhouse gas; however, large-scale monitoring remains challenging due to the high costs and spatial limitations of ground-based and airborne observations. In contrast, Sentinel-2 shortwave infrared (SWIR)–based plume detection is hindered by its coarse spectral resolution, surface artifacts, and limited real-world annotations. This study proposes a self-supervised learning (SSL) framework based on the Simple Framework for Contrastive Learning of Visual Representations (SimCLR) to learn transferable CH4 plume representations from unlabeled Sentinel-2 data. A real-world dataset of 456 Sentinel-2 image tiles was manually annotated using the multi-band–multi-pass (MBMP) approach and utilized to evaluate six encoder backbones. Across five labeled-data portions ranging from 20% to 100%, SimCLR pretraining improved plume segmentation compared to ImageNet-only initialization. In the full-data scenario, MobileNet achieved an F1-score of 0.90 with an Intersection over Union (IoU) of 0.80, while Shifted Window Transformer (SwinT) reached an F1-score of 0.85 with an IoU of 0.75. The benefit of self-supervised pretraining was most evident with limited labeled data, where ImageNet-only models degraded substantially, while SimCLR-pretrained encoders achieved higher accuracy. Moreover, the Integrated Mass Enhancement (IME) method was employed for quantifying the emission flux rate. MobileNet provided the strongest agreement with reference emission estimates, achieving an RMSE of 1690 kg/h. Finally, the results demonstrate that SimCLR-based SSL substantially enhances CH4 plume detection from Sentinel-2 imagery and supports more reliable emission quantification for large-scale CH4 monitoring.