A search has been made for supersymmetry in a final state containing two photons and missing transverse momentum using the ATLAS detector at the Large Hadron Collider. The search makes use of 3.2fb-1 of proton-proton collision data collected at a centre-of-mass energy of 13 TeV in 2015. Using a combination of data-driven and Monte-Carlo-based approaches, the Standard Model background is estimated to be 0.27-0.10+0.22 events. No events are observed in the signal region; considering the expected background and its uncertainty, this observation implies a model-independent 95 % CL upper limit of 0.93 fb (3.0 events) on the visible cross section due to physics beyond the Standard Model. In the context of a generalized model of gauge-mediated supersymmetry breaking with a bino-like next-to-lightest supersymmetric particle, this leads to a lower limit of 1650 GeV on the mass of a degenerate octet of gluino states, independent of the mass of the lighter bino-like neutralino.