Background: Numerous healthcare services have been affected by the COVID-19 pandemic worldwide. Specialized healthcare services were postponed or canceled, potentially compromising regular services for hemato-oncology patients. The current study aimed to analyze the impact of the COVID-19 pandemic on access to hemato-oncology services in Almaty, the largest city in Kazakhstan. Methods: We retrospectively analyzed the socio-demographic characteristics of patients admitted to two large tertiary centers rendering hemato-oncology services, the City Clinical Hospital 7 (H7) and the Kazakh Institute of Oncology and Radiology (KazIOR). All data were retrieved for the period spanning from 1 March 2019 to 28 February 2022. The retrieved variables included age, gender, type of residence, hospitalization rate, treatment outcomes (discharged/deceased), bed days, diagnoses according to International Classification of Diseases (ICD-10) (acute leukemia and hematopoietic depression, lymphoproliferative diseases, and myeloproliferative diseases), and referral sources (ambulance, another hospital, consultative and diagnostic assistance, primary healthcare, self-referral, and referrals from hematologists’ offices). Results: In the 2019–2022 period, 6763 hemato-oncology hospitalizations were registered: 3583 in H7 and 3180 in KazIOR. The mean age at hospitalization was 55.04 (SD = 16.07) for females and 51.2 (SD = 16.7) for males. The proportion of hospitalized urban and rural patients differed significantly: 6191 (92%) and 571 (8,4%), respectively (χ² = 13.8, p = 0.001). In the 2020–2021 period, fewer patients were discharged (n = 2047) compared to 2019–2020 (n = 2387) and 2021–2022 (n = 2081) (χ² = 20.09, p = 0.003). However, the proportion of deaths in the 2020–2021 period (3.5%) was higher than in the 2019–2020 (3.2%) and 2021–2022 periods (2.6%) (χ² = 20.09, p = 0.003). A total of 403 (19%) hospital admissions were carried out by ambulance (emergency cases) in the 2020–2021 period, 368 (14.8%) in 2019–2020, and 394 (18.3%) in 2021–2022 (χ² = 2231, p < 0.001). The number of patients transferred from other hospitals to H7 and KazIOR increased by 12.4% in the 2020–2021 period. Conclusions: Our findings indicate a negative impact of the COVID-19 pandemic on access to hemato-oncology services, leading to increased mortality. Further studies are warranted to explore factors underlying the trends in hospitalizations and mortality of hemato-oncology patients during healthcare crises.