Giant Rydberg excitons with principal quantum numbers as high as n = 25 have been observed in cuprous oxide (Cu2O), a semiconductor in which the exciton diameter can become as large as ∼1 μm. The giant dimension of these excitons results in excitonic interaction enhancements of orders of magnitude. Rydberg exciton–polaritons, formed by the strong coupling of Rydberg excitons to cavity photons, are a promising route to exploit these interactions and achieve a scalable, strongly correlated solid-state platform. However, the strong coupling of these excitons to cavity photons has remained elusive. Here, by embedding a thin Cu2O crystal into a Fabry–Pérot microcavity, we achieve strong coupling of light to Cu2O Rydberg excitons up to n = 6 and demonstrate the formation of Cu2O Rydberg exciton–polaritons. These results pave the way towards realizing strongly interacting exciton–polaritons and exploring strongly correlated phases of matter using light on a chip.