Quantum dots (QDs) grown by chemical synthesis methods are relatively unstable and present difficulties in dispersion and preservation. The most common way of surpassing the stability issues is to embed (and passivate) the QDs in a matrix material. However, some fundamental questions concerning the influence of the dielectric confinement caused by the matrix environment on the exciton energy and exciton binding energy of the QDs have not yet been properly addressed. Here we explore the exciton fine structure of wurtzite ZnO QDs by means of plane-wave million-atom atomistic pseudopotential calculations and a configuration interaction approach taking into account the dielectric confinement from the surrounding material. Our results indicate that the exciton energy increases and the exciton binding energy decreases as the dielectric constant of the surrounding material increases. The behavior of the exciton binding energy is caused by the presence of self-polarization potential induced by the dielectric mismatch in the surface of the QD. This mainly alters the localization of the hole charge density and thus reduces the electron-hole overlap and inevitably the exciton binding energy.