This letter presents the first measurement of jet mass in Pb–Pb and p–Pb collisions at s_NN=2.76 TeV and s_NN=5.02 TeV, respectively. Both the jet energy and the jet mass are expected to be sensitive to jet quenching in the hot Quantum Chromodynamics (QCD) matter created in nuclear collisions at collider energies. Jets are reconstructed from charged particles using the anti-k_T jet algorithm and resolution parameter R=0.4. The jets are measured in the pseudorapidity range |η_jet|<0.5 and in three intervals of transverse momentum between 60 GeV/c and 120 GeV/c. The measurement of the jet mass in central Pb–Pb collisions is compared to the jet mass as measured in p–Pb reference collisions, to vacuum event generators, and to models including jet quenching. It is observed that the jet mass in central Pb–Pb collisions is consistent within uncertainties with p–Pb reference measurements. Furthermore, the measured jet mass in Pb–Pb collisions is not reproduced by the quenching models considered in this letter and is found to be consistent with PYTHIA expectations within systematic uncertainties.