The recently detected γ-ray emission from starburst galaxies is most commonly considered to be diffuse emission arising from strong interactions of accelerated cosmic rays. Mannheim, Elsässer & Tibolla, however, have argued that a population of individual pulsar-wind nebulae (PWNe) could be responsible for the detected TeV emission. Here, we show that the starburst environment plays a critical role in the TeV emission from starburst PWN, and perform the first detailed calculations for this scenario. Our approach is based on the measured star formation rates in the starburst nuclei of NGC 253 and M82, assumed pulsar birth periods and a simple model for the injection of non-thermal particles. The two-zone model applied here takes into account the high far-infrared radiation field and different densities and magnetic fields in the PWN and the starburst regions, as well as particle escape. We confirm that PWN can make a significant contribution to the TeV fluxes, provided that the injection spectrum of particles is rather hard and that the average pulsar birth period is rather short (∼35 ms). The PWN contribution should lead to a distinct spectral feature which can be probed by future instruments such as Cherenkov Telescope Array.