Exposure to intimate partner violence (IPV) can have profound adverse consequences on maternal and child health. This study aimed to: (1) identify factors associated with IPV during pregnancy and postpartum in Bangladesh; and (2) assess the associations between IPV and maternal mental health and breastfeeding practices. We used data from a cross-sectional survey of 2000 mothers with children <6 months in four districts in Bangladesh. We applied multivariable logistic regression models to examine factors associated with IPV and structural equation modelling to assess the inter-relationships between IPV, maternal common mental disorders (CMD, measured by Self-reporting Questionnaire ≥7) and breastfeeding practices. Overall, 49.7% of mothers experienced violence during the last 12 months and 28% of mothers had high levels of CMD. Only 54% of women reported early initiation of breastfeeding and 64% reported exclusive breastfeeding. Women were more likely to experience IPV if living in food-insecure households, being of low socio-economic status, having low autonomy or experiencing inequality in education compared with husbands (OR ranged from 1.6 to 2.8). Women exposed to IPV were 2–2.3 times more likely to suffer from high levels of CMD and 28–34% less likely to breastfeed their babies exclusively. The indirect path (the indirect effects of IPV on breastfeeding through CMD) through maternal CMD accounted for 14% of the relationship between IPV on breastfeeding practice. In conclusion, IPV is pervasive in Bangladesh and is linked to increased risks of CMD and poor breastfeeding practices. Integrating effective interventions to mitigate IPV, along with routine maternal and child health services and involving men in counselling services, could help both to reduce exposure to IPV among women and to contribute to better health outcomes for women and children.