Background: Unsafe medication practices are the leading causes of avoidable patient harm in healthcare systems across the world. The largest proportion of which occurs during medication administration. Nurses play a significant role in the occurrence as well as preventions of medication administration errors. However, only a few relevant studies explored the problem in Ethiopia. Therefore, this study aimed to assess the magnitude and contributing factors of medication administration error among nurses in tertiary care hospitals, Addis Ababa, Ethiopia, 2018. Methods: We conducted a hospital-based, cross-sectional study in Addis Ababa, Ethiopia. The study involved 298 randomly selected nurses. We used adopted, self-administered survey questionnaire and checklist to collect data via self-reporting and direct observation of nurses while administering medications. The tools were expert reviewed and tested on 5% of the study participants. We analyzed the data descriptively and analytically using SPSS version 24. We included those factors with significant p-values (p ≤ 0.25) in the multivariate logistic regression model. We considered those factors, in the final multivariate model, with p < 0.05 at 95%Cl as significant predictors of medication administration errors as defined by nurse self-report. Result: Two hundred and ninety eight (98.3%) nurses completed the survey questionnaire. Of these, 203 (68.1%) reported committing medication administration errors in the previous 12 months. Factors such as the lack of adequate training [AOR = 3.16; 95% CI (1.67,6)], unavailability of a guideline for medication administration [AOR = 2.07; 95% CI (1.06,4.06)], inadequate work experience [AOR = 6.48; 95% CI (1.32,31.78)], interruption during medication administration [AOR = 2.42, 95% CI (1.3,4.49)] and night duty shift [AOR = 5, 95% CI (1.82, 13.78)] were significant predictors of medication administration errors at p-value < 0.05. Conclusion and recommendation: Medication administration error prevention is complex but critical to ensure the safety of patients. Based on our study, providing a continuous training on safe administration of medications, making a medication administration guideline available for nurses to apply, creating an enabling environment for nurses to safely administer medications, and retaining more experienced nurses may be critical steps to improve the quality and safety of medication administration.