This paper describes a search for dark photons ( γ _d ) in proton-proton collisions at $$ \sqrt{s} $$ s = 13 TeV at the Large Hadron Collider (LHC). The dark photons are searched for in the decay of Higgs bosons ( H → γγ _d ) produced through the ZH production mode. The transverse mass of the system, made of the photon and the missing transverse momentum from the non-interacting γ _d , presents a distinctive signature as it peaks near the Higgs boson mass. The results presented use the total Run-2 integrated luminosity of 139 fb ^{− 1} recorded by the ATLAS detector at the LHC. The dominant reducible background processes are estimated using data-driven techniques. A Boosted Decision Tree technique is adopted to enhance the sensitivity of the search. As no excess is observed with respect to the Standard Model prediction, an observed (expected) upper limit on the branching ratio BR( H → γγ _d ) of 2.28% ( $$ {2.82}_{-0.84}^{+1.33}\% $$ 2.82 − 0.84 + 1.33 % ) is set at 95% CL for massless γ _d . For massive dark photons up to 40 GeV, the observed (expected) upper limits on BR( H → γγ _d ) at 95% confidence level is found within the [2.19,2.52]% ([2.71,3.11]%) range.