Live attenuated vaccines against mumps virus (MuV) have been traditionally produced by passaging the virus in the embryonated chicken eggs or primary chicken embryo fibroblasts (CEFs). Virus propagation on these cell substrates enables successful virus attenuation and retains it sufficiently antigenic to induce lasting protective immunity in humans. The aim of this study was to identify critical factors for MuV replication in primary CEFs grown on a small-scale level in order to explore possibilities for improvements in the virus replication and yield. The effect of differently prepared cells, culturing conditions, and infection conditions on virus yield was estimated by employing statistical design of experiments (DoE) methodology. Our results show that the preparation of primary CEFs and the way of their infection substantially impact virus yield and are critical for efficient MuV replication. These process parameters should be considered in further process optimization. We also demonstrate the applicability of DoE in optimization of virus replication as a crucial step in obtaining high virus yields.