A search is presented for exotic decays of a Higgs boson into undetectable particles and one or two isolated photons in pp collisions at a center-of-mass energy of 8 TeV. The data correspond to an integrated luminosity of up to 19.4 fb(-1) collected with the CMS detector at the LHC. Higgs bosons produced in gluon-gluon fusion and in association with a Z boson are investigated, using models in which the Higgs boson decays into a gravitino and a neutralino or a pair of neutralinos, followed by the decay of the neutralino to a gravitino and a photon. The selected events are consistent with the background-only hypothesis, and limits are placed on the product of cross sections and branching fractions. Assuming a standard model Higgs boson production cross section, a 95% confidence level upper limit is set on the branching fraction of a 125 GeV Higgs boson decaying into undetectable particles and one or two isolated photons as a function of the neutralino mass. For this class of models and neutralino masses from 1 to 120 GeV an upper limit in the range of 7 to 13% is obtained. Further results are given as a function of the neutralino lifetime, and also for a range of Higgs boson masses. (C) 2015 CERN for the benefit of the CMS Collaboration. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).