A measurement of the energy density in proton–proton collisions at a centre-of-mass energy of √s = 13 TeV is presented. The data have been recorded with the CMS experiment at the LHC during low luminosity operations in 2015. The energy density is studied as a function of pseudorapidity in the ranges -6.6 < η < -5.2 and 3.15 < |η| < 5.20. The results are compared with the predictions of several models. All the models considered suggest a different shape of the pseudorapidity dependence compared to that observed in the data. A comparison with LHC proton–proton collision data at √s = 0.9 and 7 TeV confirms the compatibility of the data with the hypothesis of limiting fragmentation.