We present a signature-based search for the anomalous production of events containing a photon, two jets, of which at least one is identified as originating from a b quark, and missing transverse energy (E̸T). The search uses data corresponding to 2.0  fb−1 of integrated luminosity from pp collisions at a center-of-mass energy of s√=1.96  TeV, collected with the CDF II detector at the Fermilab Tevatron. From 6.697 47×106 events with a photon candidate with transverse energy ET>25  GeV, we find 617 events with E̸T>25  GeV and two or more jets with ET>15  GeV, at least one identified as originating from a b quark, versus an expectation of 607±113 events. Increasing the requirement on E̸T to 50 GeV, we find 28 events versus an expectation of 30±11 events. We find no indications of non-standard-model phenomena.