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Few studies have investigated whether SARS-CoV-2 infections increase the incidence of dengue haemorrhagic fever/shock syndrome (DHF/DSS) and/or severe dengue (SD) in dengue virus (DENV)-infected patients. This study was performed on a site with high incidences of classical dengue, but relatively few DHF/DSS or SD cases as defined by the WHO 1997 or 2009 criteria, respectively. Clinical, haematological/biochemical, and viral diagnostic data were collected from febrile patients before, during, and after the COVID-19 epidemic to assess whether (a) DENV-infected patients with prior SARS-CoV-2 infections or (b) DENV-SARS-CoV-2-co-infected patients had increased incidences of SD/DHF/DSS using logistic regression and machine learning models. Higher numbers of DHF/DSS/SD occurred during the COVID-19 epidemic, particularly in males and 18–40-year-olds. Significantly increased symptoms in the DENV-SARS-CoV-2-co-infected cases were (a) haemoconcentration (p < 0.0009) and hypotension (p < 0.0005) (DHF/DSS and SD criteria), (b) thrombocytopenia and mucosal bleeding (DHF/DSS-criteria), (c) abdominal pain, persistent vomiting, mucosal bleeding, and thrombocytopenia (SD warning signs) and (d) dyspnoea, but without fluid accumulation. DENV-infected patients with prior SARS-CoV-2 infections had significantly increased incidences of thrombocytopenia (DHF/DSS-criteria) and/or abdominal pain and persistent vomiting and also thrombocytopenia (SD warning signs), but without significant haemoconcentration or hypotension. DENV-SARS-CoV-2 co-infections significantly increased the incidence of DHF/DSS/SD, while DENV-infected patients with prior SARS-CoV-2 infections displayed significantly increased incidences of thrombocytopenia (DHF/DSS-criteria) and three important SD warning signs, which are therefore very important for health workers/clinicians in assessing patients’ DHF/DSS/SD risk factors and planning their optimal therapies.