The results of a search for new physics in final states with photons and missing transverse energy are reported. The study is based on a sample of proton-proton collisions collected at a center-of-mass energy of 13 TeV with the CMS detector in 2015, corresponding to an integrated luminosity of 2.3 inverse femtobarns. Final states with two photons and significant missing transverse energy are used to search for supersymmetric particles in models of supersymmetry (SUSY) with general gauge-mediated (GGM) supersymmetry breaking. No excess is observed with respect to the standard model expectation, and the results are used to set limits on gluino pair production and squark pair production in the GGM SUSY framework. Gluino masses below 1.65 TeV and squark masses below 1.37 TeV are excluded at a 95% confidence level.