(1) Background: When the Omicron variant of SARS-CoV-2 first emerged in Germany in January 2022, data on related disease severity among children and adolescents were not yet available. Given Omicron’s high transmissibility, the ability to assess its impact on admission and hospitalization rates in children’s hospitals is critical for the purpose of understanding the scope of its burden on the German healthcare system. (2) Methods: From 24 January 2022 to 31 July 2022, SARS-CoV-2 cases admitted to German pediatric hospitals were monitored via a national, clinician-led reporting system (CLRS) established by the German Society for Pediatric Infectious Diseases (DGPI). Cases treated on general wards and intensive care units, as well as patient age and the need for respiratory support, were recorded. (3) Results: From January to July 2022, a median of 1.7 cases (range 0.4–3) per reporting pediatric hospital per day was hospitalized in general wards, whereas a median of 0.1 cases (range 0–0.4 cases) was admitted to intensive care units. Of all hospitalized patients, 4.2% received respiratory support. (4) Conclusions: Despite the high incidence rates documented in connection with the Omicron variant in early 2022, the number of pediatric hospital admissions, and especially the number of cases with the need for intensive care treatment and respiratory support due to symptomatic SARS-CoV-2 infection, remained relatively low. Higher Omicron incidence rates had only a modest impact on SARS-CoV-2-related admissions and hospitalization in German children’s hospitals.