Background Rational drug use requires that patients receive and take medication appropriately. Though the process of diagnosis and pharmaceutical care is complex, World Health Organization (WHO)/international network for rational use of drugs (INRUD) core drug use indicators investigate drug use to minimize the hazardous effect of the drug and enhance the wise use of scares resources. This study assessed drug use patterns in health centers of Dessie town using WHO/INRUD indicators. Methods A cross-sectional study was conducted in public health centers of Dessie town. Data were retrospectively collected from 1500 prescriptions dispensed from January 1, 2018, to December 31, 2018 using WHO data collection tool to assess prescribing indicators. For patient care and health facility indicators, 600 patients and 3 health centers were prospectively reviewed. Systematic random sampling was used to select samples. Data were analyzed using the Statistical Package for the Social Sciences version 20. Results The average number of drugs per encounter was 2.1. The percentage of encounters with antibiotics and injection was 44% and 13.9%, respectively. The percentage of drugs prescribed by generic name and from an essential drug list was 98% and 100%, respectively. On average, patients spent 4.7 min for consultation and 105 s for dispensing. From 1305 prescribed drugs, 92% were dispensed, while only 4% were labeled adequately. More than half (54.8%) of patients had adequate knowledge of their medication. None of the health centers had an essential drug list. The availability of key essential medicines was 64.10%. Conclusion This study demonstrated irrational drug use practices in all healthcare facilities. Polypharmacy, antibiotics over-prescribing, short consultation and dispensing times, inadequate labeling of medicines, inadequate level of patients' knowledge about prescribed medicines, and unavailability of key drugs in stock were found to be the major problems. Continuous refreshment trainings on rational use of drugs and WHO recommendations should be given for prescribers and pharmacists. Further, we recommend studies involving large number of facilities to estimate overall prescribing practices.