Objective Globally, 13–20% of women experience a common mental disorder (CMD) postnatally. Unfortunately, the burden of CMDs is disproportionally substantial in women from low-income countries. Nevertheless, there is a growing recognition of the buffering effect of social support (SS) on psychiatric morbidity and the need for mental well-being support services/interventions. This study evaluated the relationship between psychiatric morbidity and SS levels, and factors influencing the mental health functioning of Zimbabwean women postnatally. Data were collected from 340 mothers and were analysed through structural equation modelling. Results The mothers’ mean age was 26.6 (SD 5.6) years. The mean Multidimensional Scale of Perceived Social Support score was 42.7 (SD 10.8), denoting high levels of SS. Additionally, 29.1% of the population reported excessive psychiatric morbidity, the median Shona Symptoms Questionnaire score was 5 (IQR: 2–8). The structural equation model demonstrated the buffering effects of SS on psychiatric morbidity (r = − 0.585, p = 0.01), and accounted for 70% of the variance. Being unmarried, increased maternal age, lower educational and income levels were associated with poorer maternal mental health. There is a need for routine; surveillance and treatment of CMDs in women in the postnatal period, including integration of low-cost, evidenced-based and task-shifting SS interventions. Electronic supplementary material The online version of this article (10.1186/s13104-019-4151-1) contains supplementary material, which is available to authorized users.