Accurately quantifying cellular morphology at scale could substantially empower existing single-cell approaches. However, measuring cell morphology remains an active field of research, which has inspired multiple computer vision algorithms over the years. Here, we show that DINO, a vision-transformer based, self-supervised algorithm, has a remarkable ability for learning rich representations of cellular morphology without manual annotations or any other type of supervision. We evaluate DINO on a wide variety of tasks across three publicly available imaging datasets of diverse specifications and biological focus. We find that DINO encodes meaningful features of cellular morphology at multiple scales, from subcellular and single-cell resolution, to multi-cellular and aggregated experimental groups. Importantly, DINO successfully uncovers a hierarchy of biological and technical factors of variation in imaging datasets. The results show that DINO can support the study of unknown biological variation, including single-cell heterogeneity and relationships between samples, making it an excellent tool for image-based biological discovery.