Child abuse is a global public health problem and a serious social issue in Japan. Social support is beneficial for parents faced with childrearing challenges. The aim of this study was to clarify the association between social support and child abuse potential. A cross-sectional study was conducted using a structured questionnaire. The target population was mothers of children at nine public nursery schools. Bivariate and multiple linear regression analysis were performed to examine the effects of socio-demographic, social support and psychological distress factors on child abuse potential. Among 309 mothers, 29 (9.4%) had a high child abuse potential score. Bivariate analysis indicated that mothers with a higher child abuse potential score were more likely to be divorced or unmarried (P < 0.001); living in single-female-parent households (P < 0.001); have low perceived economic status (P < 0.001); have a low level of child care support (P = 0.01); have a low Multidimensional Scale of Perceived Social Support (MSPSS) score (P < 0.001); and/or a high General Health Questionnaire-12 score (GHQ-12) (P < 0.001). Important predictors of child abuse potential among the mothers surveyed included living in single-female-parent households, having low perceived economic status, low MSPSS score, and high GHQ-12 score. Improving approaches that help mothers build social support relationships and ease them into child rearing in a psychologically healthy condition is recommended to prevent child abuse.