Abstract Objective Influenza viruses are among the most common respiratory pathogens for all age groups, and may cause seasonal outbreaks. The aim of our study was to describe the clinical characteristics of influenza cases in the 2019–2020 flu season and to study the risk factors for hospital admission and complications. Methods This was a retrospective study in 251 children (group 1: nonhospitalized; group 2: hospitalized) with influenza in the 2019–2020 flu season. Data on demographic features, influenza type, complaints, complications, and hospitalization length were collected and recorded. Results Influenza A was detected in 199 (79.3%) patients, and influenza B was detected in 52 (20.7%); 43.4% of patients were girls and 56.6% were boys. The mean age of the patients was 3.91 ± 3.3 years (16 days to 18 years). A total of 52 (20.7%) patients were hospitalized. The age of the patients in group 2 was lower than that in group 1 (3.1 vs. 4.2 years, p = 0.03). Group 2 patients were more likely to have creatine kinase (CK) elevation, febrile seizures, and physical examination abnormalities. Group 2 patients were also more likely to have influenza A. Patients with febrile seizures, chronic diseases, abnormal physical examination findings, developed complications, and additional drug use apart from oseltamivir in the treatment were also more likely to require hospitalization. Conclusion Infants and children with chronic diseases, history of febrile seizures, complications, and the use of drugs other than antiviral drugs should be carefully evaluated in case they need hospitalization. Increasing vaccination rates, initiation of antiviral treatment for selected patients, and close monitoring of patients in risk groups can decrease morbidity and mortality. Myalgias are a common complaint in patients with acute influenza infection. Previous studies suggest CK measurement be part of the work-up for the hospitalized patient with acute influenza infection.