Background Neonatal mortality remains a public health problem in the developing world. Globally, around 2.5 million neonatal deaths are reported annually with the highest mortality concentrated in sub-Saharan Africa and South Asia. In comparison with countries demonstrating the lowest neonatal mortality, the risk of mortality is over 30 times higher in sub-Saharan Africa. Ethiopia is among the countries with a high neonatal mortality rate, and the burden of this mortality remains unreported in many pastoralist areas such as Somali Regional State, Eastern Ethiopia. We aimed to investigate factors associated with neonatal mortality in public Hospitals of the Somali Regional State in Eastern Ethiopia. Methods A facility-based cross-sectional study was conducted from May 1st to 30th, 2020 in three public Hospitals of Somali Regional State in Eastern Ethiopia. A total of 510 neonates admitted to neonatal intensive care units from January 2018 to December 2019 were enrolled in the study. The charts of neonates were randomly selected and retrieved. Data were collected using a pretested and validated structured questionnaire. The collected were entered into Epidata version 3.1 and exported to SPSS version 22 (IBM SPSS Statistics, 2013) for further analysis. Descriptive statistics were carried out using frequency tables, proportions, and summary measures. Predictors were assessed using a multivariable logistic regression analysis model and reported using adjusted odds ratio (AOR) with 95% Confidence Interval (CI). Statistical significance was considered at a p-value <0.05. Results Overall, the neonatal mortality was 18.6% [95%CI (15.31, 22.30)], equating to a rate of 186 per 1000 live births. The most common causes of mortality were prematurity (44.6%), low birth weight (33.5%), and birth asphyxia (27.6%). In the final model of multivariable analysis, predictors such as: lack of antenatal care follow-up[AOR = 3.71, 95%CI (2.13, 6.44)], neonatal sepsis [AOR = 1.84, 95%CI (1.07, 3.19], preterm birth [AOR = 2.20, 95%CI (1.02, 4.29], and birth asphyxia [AOR = 2.40, 95%CI(1.26,4.43)], and birth weight of less than 2500gms[AOR = 3.40, 95%CI(1.92, 6.01)] were statistically associated with neonatal mortality. Conclusion In this study, the neonatal mortality rate was high compared to national and global targets because one in five neonates dies due to preventable causes. Modifiable and non-modifiable risk factors were identified as predictors. This result calls for all stakeholders to provide due attention to low birth weight and premature babies. Early identification and management of birth asphyxia and neonatal sepsis are also very crucial to reduce the risks of neonatal deaths.