We report the first observation of the radiative charm decay D^{0}→ρ^{0}γ and the first search for CP violation in decays D^{0}→ρ^{0}γ, ϕγ, and K[over ¯]^{*0}(892)γ, using a data sample of 943 fb^{-1} collected with the Belle detector at the KEKB asymmetric-energy e^{+}e^{-} collider. The branching fraction is measured to be B(D^{0}→ρ^{0}γ)=(1.77±0.30±0.07)×10^{-5}, where the first uncertainty is statistical and the second is systematic. The obtained CP asymmetries A_{CP}(D^{0}→ρ^{0}γ)=+0.056±0.152±0.006, A_{CP}(D^{0}→ϕγ)=-0.094±0.066±0.001, and A_{CP}(D^{0}→K[over ¯]^{*0}γ)=-0.003±0.020±0.000 are consistent with no CP violation. We also present an improved measurement of the branching fractions B(D^{0}→ϕγ)=(2.76±0.19±0.10)×10^{-5} and B(D^{0}→K[over ¯]^{*0}γ)=(4.66±0.21±0.21)×10^{-4}.