The photon polarization in b→sγ transitions is measured for the first time in radiative b-baryon decays exploiting the unique spin structure of Λb0→Λγ decays. A data sample corresponding to an integrated luminosity of 6 fb-1 collected by the LHCb experiment in pp collisions at a center-of-mass energy of 13 TeV is used. The photon polarization is measured to be αγ=0.82-0.26-0.13+0.17+0.04, where the first uncertainty is statistical and the second systematic. This result is in agreement with the Standard Model prediction and previous measurements in b-meson decays. Charge-parity breaking effects are studied for the first time in this observable and found to be consistent with CP symmetry.