Micropillars of different diameters have been prepared by focused ion beam milling out of a planar ZnTe-based cavity. The monolithic epitaxial structure, deposited on a GaAs substrate, contains CdTe quantum dots embedded in a ZnTe λ-cavity delimited by two distributed Bragg reflectors (DBRs). The high refractive index material of the DBR structure is ZnTe, while for the low index material a short-period triple MgTe/ZnTe/MgSe superlattice is used. The CdTe quantum dots are formed by a novel Zn-induced formation process and are investigated by scanning transmission electron microscopy. Micro-photoluminescence measurements show discrete optical modes for the pillars, in good agreement with calculations based on a vectorial transfer matrix method. The measured quality factor reaches a value of 3100.