The human adenovirus (HAdV) is a common pathogen in children that can cause acute respiratory virus infection (ARVI). However, the molecular epidemiological and clinical information relating to HAdV among hospitalized children with ARVI is rarely reported in Russia. A 4-year longitudinal (2019–2022) study among hospitalized children (0–17 years old) with ARVI in Novosibirsk, Russia, was conducted to evaluate the epidemiological and molecular characteristics of HAdV. Statistically significant differences in the detection rates of epidemiological and virological data of all positive viral detections of HAdV were analyzed using a two-tailed Chi-square test. The incidence of HAdV and other respiratory viruses such as human influenza A and B viruses, respiratory syncytial virus, coronavirus, parainfluenza virus, metapneumovirus, rhinovirus, bocavirus, and SARS-CoV-2 was investigated among 3190 hospitalized children using real-time polymerase chain reaction. At least one of these respiratory viruses was detected in 74.4% of hospitalized cases, among which HAdV accounted for 4%. A total of 1.3% co-infections with HAdV were also registered. We obtained full-genome sequences of 12 HAdVs, which were isolated in cell cultures. Genetic analysis revealed the circulation of adenovirus of genotypes C1, C2, C5, C89, and 108 among hospitalized children in the period from 2019–2022.