We sought to explore mental health and psychosocial impact among young people (18 to 24 years old) in Bogotá during the first months of the COVID-19 pandemic. Methods: We carried a cross sectional study using a web-based survey to assess mental health and personal impact among 18 to 24 years old living in Bogotá during the first 4 months of the 2020 COVID-19 pandemic lockdown. The depressive symptoms were measured with PHQ-8 and anxiety symptoms with (GAD-7). We also designed a questionnaire exploring changes in personal, family and social life. Results: Overall, 23% of the sample (n = 834) reported mild depressive symptoms (males 24% and females 23%); 29% reported moderate depressive symptoms (males 28%, females 30%); 22% moderate-severe symptoms (males 20%, females 23%) and 17% severe symptoms (males 15%, females 17%). Mild anxiety symptoms were reported by 29% of the sample (males 30%, females 29%); moderate anxiety symptoms by 29% (males 26%, females 30%); moderate-severe 18% (males 15%, females 20%) and severe anxiety by 6.0% (males 6.0% and females 6.0%). High symptoms of depression (PHQ-8 ≥ 10) were associated with being female, considering that the quarantine was stressful, having one member of the family losing their job, worsening of family relationships, decrease of physical activity and having a less nutritious diet. Having high anxiety symptoms (GAD-7 ≥ 10) were associated with sometimes not having enough money to buy food. Conclusions: The first months of the pandemic lockdown were associated with high depressive and anxiety symptoms among young persons living in Bogotá, Colombia. Increasing public health measures to provide support for young people is needed during lockdowns and it is necessary to further explore the long-term mental health impact due to personal, family and social changes brought by the COVID-19 pandemic.