We report a study of the process e^{+}e^{-}→(D^{*}D[over ¯]^{*})^{0}π^{0} using e^{+}e^{-} collision data samples with integrated luminosities of 1092 pb^{-1} at sqrt[s]=4.23 GeV and 826 pb^{-1} at sqrt[s]=4.26 GeV collected with the BESIII detector at the BEPCII storage ring. We observe a new neutral structure near the (D^{*}D[over ¯]^{*})^{0} mass threshold in the π^{0} recoil mass spectrum, which we denote as Z_{c}(4025)^{0}. Assuming a Breit-Wigner line shape, its pole mass and pole width are determined to be (4025.5_{-4.7}^{+2.0}±3.1) MeV/c^{2} and (23.0±6.0±1.0) MeV, respectively. The Born cross sections of e^{+}e^{-}→Z_{c}(4025)^{0}π^{0}→(D^{*}D[over ¯]^{*})^{0}π^{0} are measured to be (61.6±8.2±9.0) pb at sqrt[s]=4.23 GeV and (43.4±8.0±5.4) pb at sqrt[s]=4.26 GeV. The first uncertainties are statistical and the second are systematic.