Currently, there are no therapies to prevent severe dengue disease. Essential oils (EOs) can serve as primary sources for research and the discovery of phytomedicines for alternative therapy. Fourteen EOs samples were obtained by distillation from six plants used in Colombian folk medicine. GC/MS analysis identified 125 terpenes. Cytopathic effect (CPE) reduction assays revealed differences in antiviral activity. EOs of Lippia alba, citral chemotype and carvone-rich fraction; Lippia origanoides, phellandrene chemotype; and Turnera diffusa, exhibited strong antiviral activity (IC50: 29 to 82 µg/mL; SI: 5.5 to 14.3). EOs of Piper aduncum, Ocimum basilicum, and L. origanoides, carvacrol, and thymol chemotypes, exhibited weak antiviral activity (32 to 53% DENV-CPE reduction at 100 µg/mL; SI > 5.0). Cluster and one-way ANOVA analyses suggest that the strong antiviral activity of EOs could be attributed to increased amounts of non-phenolic oxygenated monoterpenes and sesquiterpene hydrocarbons. Docking analyses (AutoDock Vina) predicted binding affinity between the DENV-2 E protein and terpenes: twenty sesquiterpene hydrocarbons (−8.73 to −6.91 kcal/mol), eight oxygenated monoterpenes (−7.52 to −6.98 kcal/mol), and seven monoterpene hydrocarbons (−7.60 to −6.99 kcal/mol). This study reports for the first time differences in the antiviral activity of EOs against DENV, corresponding to their composition of monoterpenes and sesquiterpenes.