A search for a narrow diphoton mass resonance is presented based on data from 3.0  fb−1 of integrated luminosity from pp collisions at s√=1.96  TeV collected by the CDF experiment. No evidence of a resonance in the diphoton mass spectrum is observed, and upper limits are set on the cross section times branching fraction of the resonant state as a function of Higgs boson mass. The resulting limits exclude Higgs bosons with masses below 106  GeV/c2 at a 95% Bayesian credibility level for one fermiophobic benchmark model.