The present work details the occurrence of the Kelvin–Helmholtz instability in a centrifugal compressor operating near stall. The analysis is based on unsteady three-dimensional simulations performed on a calculation domain covering the full annulus for the impeller and the vaned diffuser. A detailed investigation of the flow structure is presented, together with its evolution consequent to the mass flow reduction. It is demonstrated that this reduction leads to an enlargement of the low-momentum flow region initially induced by the combination of the secondary and leakage flows. When the compressor operates near stall, the shear layer at the interface between the main flow and this low-momentum flow becomes unstable and induces a periodic vortex shedding. The frequency of such an unsteady phenomenon is not correlated with the blade-passing frequency. Its signature is thus easily isolated from the deterministic rotor/stator interaction. Its detection requires full-annulus simulations with an accurate resolution in time and space, which explains why it has never been previously observed in centrifugal compressors.