A search is performed for long-lived neutral particles decaying into a photon and invisible particles. An example of such a signature is the decay of the lightest neutralino with nonzero lifetime into a gravitino and a photon in gauge-mediated supersymmetry, with the neutralino as the next-to-lightest supersymmetric particle and the gravitino as the lightest. The search uses events containing photons, missing transverse energy, and jets. The impact parameter of the photon relative to the beam-beam collision point can be reconstructed using converted photons. The method is sensitive to lifetimes of the order of 0.1 to ins. The data sample corresponds to an integrated luminosity of 2.23 fb(-1) in pp collisions at root s = 7 TeV, recorded in the first part of 2011 by the CMS experiment at the LHC. Cross-section limits are presented on pair production for such particles, each of which decays into a photon and invisible particles. The observed 95% confidence level limits vary between 0.11 and 0.21 pb, depending on the neutral particle lifetime.