Classification of weather systems provides a simple description of atmospheric circulations and bridges the gap between large-scale atmospheric conditions and local-scale environmental variables. However, the existing classification methods are challenged due to lack of labels and inaccurate similarity measures between data samples. In this letter, we propose a self-supervised Spatiotemporal Contrastive Learning (SCL) framework for the classification of weather systems without manual labels. In particular, we operate both spatial and temporal augmentation on multivariate meteorological data to fully explore temporal context information and spatial stability in accordance with synoptic nature. With the classification results, we apply a statistical downscaling method based on analog forecasting for the assessment and comparison of classification results. The experimental results demonstrate that the proposed SCL model outperforms traditional classification methods.