Aim and background: Pandemics are known to have effects on the mental health of the populace. Studies on the effect of coronavirus disease-19 (COVID-19) on the general population have brought out the psychological effects of the pandemic. However, the psychosocial impact of COVID-19 on pregnant and postnatal women has not been assessed. The study aimed was to assess the level of psychosocial stress in postnatal and antenatal women during the pandemic and its association of various sociodemographic and pregnancy-related factors with high fear of COVID-19 scores. Materials and methods: This cross-sectional study included antenatal and post-natal women attending the outpatient clinic. Patients were given questionnaires to document the sociodemographic details, pregnancy-related fear during a pandemic, and fear of COVID-19 scale. Results: A total of 648 women participated in the study. Among the stressors assessed, better support from the partner (n = 623), satisfactory interaction with healthcare workers (n = 627), and lower social deprivation (n = 371) was reported; the participants denied domestic abuse (n = 574) or fear of infecting the newborn (n = 482). Positive associations were observed between high fear of COVID-19 scores and sociodemographic factors like low-income status (p = 0.026), domestic abuse during lockdown (p = 0.0034), difficulty in getting together with family and friends (p = 0.0001), and adverse effect on the financial status of the family (p = 0.0008), difficulty in transport to the hospital (p = 0.007) and fear of the newborn getting affected (p = 0.0002). Conclusion: COVID-19 did not appear to negatively affect the mental health of pregnant and postnatal women or factors assessed in the present study. A high anxiety score was associated with increased anxiety and stress related to COVID-19. Clinical significance: This prospective study provides a basic idea of different risk factors that could affect psychosocial stress in antenatal and postpartum women. The study also emphasizes the importance of support from partners and interactions with healthcare workers to improve the psychosocial status of pregnant and postnatal women.