Abstract Contact guidance—the widely-known phenomenon of cell alignment induced by anisotropic environmental features—is an essential step in the organization of adherent cells, but the mechanisms by which cells achieve this orientational ordering remain unclear. Here we seeded myofibroblasts on substrates micropatterned with stripes of fibronectin and observed that contact guidance emerges at stripe widths much greater than the cell size. To understand the origins of this surprising observation, we combined morphometric analysis of cells and their subcellular components with a novel statistical framework for modelling non-thermal fluctuations of living cells. This modelling framework is shown to predict not only the trends but also the statistical variability of a wide range of biological observables including cell (and nucleus) shapes, sizes and orientations, as well as stress-fibre arrangements within the cells with remarkable fidelity. By comparing observations and theory, we identified two regimes of contact guidance: (i) guidance on stripe widths smaller than the cell size ( w ≤ 160 μm), which is accompanied by biochemical changes within the cells, including increasing stress-fibre polarisation and cell elongation, and (ii) entropic guidance on larger stripe widths, which is governed by fluctuations in the cell morphology. Overall, our findings suggest an entropy-mediated mechanism for contact guidance associated with the tendency of cells to maximise their morphological entropy through shape fluctuations.