The integrated fiducial cross-section and unfolded differential jet mass spectrum of high transverse momentum Z→bb‾ decays are measured in Zγ events in proton–proton collisions at s=13TeV. The data analysed were collected between 2015 and 2016 with the ATLAS detector at the Large Hadron Collider and correspond to an integrated luminosity of 36.1fb−1. Photons are required to have a transverse momentum pT>175GeV. The Z→bb‾ decay is reconstructed using a jet with pT>200GeV, found with the anti-kt R=1.0 jet algorithm, and groomed to remove soft and wide-angle radiation and to mitigate contributions from the underlying event and additional proton–proton collisions. Two different but related measurements are performed using two jet grooming definitions for reconstructing the Z→bb‾ decay: trimming and soft drop. These algorithms differ in their experimental and phenomenological implications regarding jet mass reconstruction and theoretical precision. To identify Z bosons, b-tagged R=0.2 track-jets matched to the groomed large-R calorimeter jet are used as a proxy for the b-quarks. The signal yield is determined from fits of the data-driven background templates to the different jet mass distributions for the two grooming methods. Integrated fiducial cross-sections and unfolded jet mass spectra for each grooming method are compared with leading-order theoretical predictions. The results are found to be in good agreement with Standard Model expectations within the current statistical and systematic uncertainties.