Rhinoviruses and respiratory enteroviruses remain among the leading causes of acute respiratory infections, particularly in children. Little is known about the genetic diversity of enteroviruses and rhinoviruses in pediatric patients with acute respiratory infections in Russia. We assessed the prevalence of human rhinoviruses/enteroviruses (HRV/EV) in 1992 children aged 0 to 17 years hospitalized with acute respiratory infections during the 2023–2024 epidemic season using PCR. The detection rate of HRV/EV was 11% (220/1992). We performed typing of 58 HRV and 28 EV viruses by partial sequencing of the VP1 gene. Rhinovirus A was the most common among HRV, followed by rhinovirus C; rhinovirus B was detected in only three cases. Enteroviruses were represented by all four species, with the EV-D68 genotype being the most frequently detected. Phylogenetic analysis of the VP1 fragment of EV-D68 showed that all our sequences belonged to the B3 subclade. We identified the first case of EV-C105 infection in Russia in a two-year-old girl hospitalized with pneumonia. Phylogenetically, the Novosibirsk strain EV-C105 was closely related to a strain discovered in France in 2018. This research helped to fill a critical gap in understanding the epidemiological landscape of HRV/EV in pediatric populations within Russia.