A search for CP violation in the decay Λ 0 → pK − μ + μ − is presented. This decay is mediated by flavour-changing neutral-current transitions in the Standard Model and is potentially sensitive to new sources of CP violation. The study is based on a data sample of proton-proton collisions recorded with the LHCb experiment, corresponding to an integrated luminosity of 3 fb−1. The Λ 0 → pK − μ + μ − decay is observed for the first time, and two observables that are sensitive to different manifestations of CP violation are measured, $$ \Delta {\mathcal{A}}_{CP}\equiv {\mathcal{A}}_{CP}\left({\Lambda}_b^0\to p{K}^{-}{\mu}^{+}{\mu}^{-}\right)-{\mathcal{A}}_{CP}\left({\Lambda}_b^0\to p{K}^{-}J/\psi \right) $$ and a $$ {a}_{CP}^{\widehat{T}\hbox{-} odd} $$ , where the latter is based on asymmetries in the angle between the μ + μ − and pK − decay planes. These are measured to be $$ \begin{array}{l}\Delta {\mathcal{A}}_{CP}=\left(-3.5\pm 5.0\left(\mathrm{stat}\right)\pm 0.2\left(\mathrm{syst}\right)\right)\times {10}^{-2},\hfill \\ {}{a}_{CP}^{\widehat{T}\hbox{-} odd}=\left(1.2\pm 5.0\left(\mathrm{stat}\right)\pm 0.7\left(\mathrm{syst}\right)\right)\times {10}^{-2},\hfill \end{array} $$ and no evidence for CP violation is found.