We report on the observation of zero-dimensional (0D) excitonic confinement in locally strained Zn1-xCdxSe quantum wells. Strain fields from self-organized CdSe quantum dots are used to locally modulate the band structure of a nearby quantum well in a heterostructure, resulting in confinement in all three dimensions. The 0D nature of excitonic confinement is verified by the observation of sharp lines in photoluminescence (PL) spectra. The temperature dependence of the PL lifetime is markedly different than that of the CdSe quantum dots. High-resolution spectra show that the PL lines from the localized states are split into linearly polarized doublets.