The influx of massive amounts of new data from current and upcoming cosmological surveys necessitates compression schemes that can efficiently summarize the data with minimal loss of information. We investigate the potential of self-supervised machine learning to construct optimal summaries of cosmological datasets. Using a particular self-supervised machine learning method, VICReg (Variance-Invariance-Covariance Regularization) deployed on lognormal random fields as well as hydrodynamical cosmological simulations, we find that self-supervised learning can deliver highly informative summaries which can be used for downstream tasks, including providing precise and accurate constraints when used for parameter inference. Our results indicate that self-supervised machine learning techniques offer a promising new approach for cosmological data compression and analysis.