This Letter presents the first measurements of the groomed jet radius Rg and the jet girth g in events with an isolated photon recoiling against a jet in lead-lead (PbPb) and proton-proton (pp) collisions at the LHC at a nucleon-nucleon center-of-mass energy of 5.02 TeV. The observables Rg and g provide a quantitative measure of how narrow or broad a jet is. The analysis uses PbPb and pp data samples with integrated luminosities of 1.7 nb−1 and 301 pb−1, respectively, collected with the CMS experiment in 2018 and 2017. Events are required to have a photon with transverse momentum pTγ>100 GeV and at least one jet back-to-back in azimuth with respect to the photon and with transverse momentum pTjet such that pTjet/pTγ>0.4. The measured Rg and g distributions are unfolded to the particle level, which facilitates the comparison between the PbPb and pp results and with theoretical predictions. It is found that jets with pTjet/pTγ>0.8, i.e., those that closely balance the photon pTγ, are narrower in PbPb than in pp collisions. Relaxing the selection to include jets with pTjet/pTγ>0.4 reduces the narrowing of the angular structure of jets in PbPb relative to the pp reference. This shows that selection bias effects associated with jet energy loss play an important role in the interpretation of jet substructure measurements.