A search for long-lived neutral particles decaying into a photon and invisible particles is performed. In the context of gauge mediated supersymmetry with the lightest neutralino as the next-to-lightest supersymmetric particle and the gravitino as the lightest supersymmetric particle, the neutralino can decay into a gravitino and a photon with a nonzero lifetime. 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 $\mathcal{O}$(0.1 ns). The data sample corresponds to an integrated luminosity of 2.1 \pm 0.1~\rm{fb^{-1}} recorded in the first part of 2011 by the CMS experiment at the LHC at $\sqrt{s}$ = 7 TeV. The search is performed using events containing photons, missing transverse energy and jets. Upper limits at the $\rm{95\%}$ confidence level are presented on the cross section for such particles from pair-production, each of which decays into a photon and invisible particles.