Background Maternal depression is known to be associated with anxiety, depression, oppositional and conduct disorders, neurocognitive deficits, ADHD, substance abuse, and personality disorder in the offspring. We aimed to describe the proportion of psychological problems among children of mothers with depression in Sri Lanka and to describe the associated sociodemographic factors. Methods A cross-sectional descriptive study was conducted on 100 children and adolescents between 4 and 16 years, whose mothers have a diagnosis of depression and are currently in remission. Specifically designed instruments were used to extract sociodemographic details and data on mother's illness. Strengths and Difficulties Questionnaire (SDQ) was used to detect psychological problems in children. Results 14% of the children scored abnormally high in hyperactivity, 13% in conduct problems, 12% in emotional problems, 9% in peer problems, and 10% in total difficulties. Children (4–12 years) scored significantly higher than the adolescents in hyperactivity and externalizing problems (p < 0.05). Significant differences were also found in peer problems (p < 0.05), internalizing problems (p < 0.05), and total difficulties (p < 0.05) in relation to the age of the mother. Conclusion Screening the children of mothers with depression for psychological problems and developing a holistic management plan, which includes measures to ensure their wellbeing, is important.