The first search for the rare radiative decay $\Xi b-\to \Xi -\gamma$ is performed using data collected by the LHCb experiment in proton-proton collisions at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 5.4 fb$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$. The $\Xi b-\to \Xi -J/\psi$ channel is used as normalization. No $\Xi b-\to \Xi -\gamma$ signal is found and an upper limit of at 95% confidence level is obtained.