Introduction Anemia is a common hematological problem in neonatal admissions. Poor detection rate and inappropriate treatment adversely affect the growing infant. Data on the magnitude and risk factors of anemia in sick newborns are lacking in Ethiopia, so knowing the prevalence and risk factors may reduce the long-term untreated complications of anemia. Objective The overall aim of this study was to assess the prevalence and associated factors of anemia among newborns admitted to Tibebe Ghion specialized hospital. Methods A hospital-based cross-sectional study was conducted among 272 newborns admitted to Tibebe Ghion Specialized Hospital from February 1 to May 30, 2021. A pretested structured questionnaire containing socio-demographic, clinical, and laboratory parameters was used for the data collection. Data were collected by trained nurses and residents after obtaining ethical clearance. The data were entered through Epi-data version 4.6 and analyzed using SPSS version 23.0 computer software. Descriptive statistics were performed using frequency, mean and standard deviation. Bivariable and multivariable binary logistic regressions were done to identify risk factors of anemia. Adjusted odds ratio with 95% confidence interval at a p-value <0.05 was declared as a statistically significant variable in the multivariable logistic regression. Results About two-thirds 177 (65.1%) of the newborn babies were male and 152 (55.9%) of the newborn had a birth weight of ≥2500 grams. The most commonly diagnosed medical conditions were sepsis 218 (80.1%) and prematurity of birth 78 (28.7%). The prevalence of anemia among newborns in this study was 63 (23.2%) [19.1–28.7%]. Gestational age of 33–36 weeks (AOR=0.36: 95% CI=0.17–0.96) and maternal anemia (AOR=3.81: 95% CI=1.29–11.23) were significantly associated with newborn anemia. Conclusion The prevalence of anemia among newborns in Tibebe Ghion specialized hospital was high. Gestational age and maternal anemia were significantly associated with newborn anemia. So, it is better to properly educate and advise women about newborn anemia during antenatal care follow-up.