Few studies have been conducted on multimorbidity (two or more chronic diseases) and rational geriatric prescribing in Africa. This study examined the prevalence and determinants of multimorbidity, polypharmacy (five or more long-term medications), and potentially inappropriate medication (PIM) use according to the 2019 Beers criteria among the older adults attending chronic care clinics from a single institution in Ethiopia. A hospital-based cross-sectional study was conducted among 320 randomly selected older adults from 12 March 2020 to 30 August 2020. A multivariable logistic regression analysis was performed to identify the predictor variables. The prevalence of multimorbidity, polypharmacy, and PIM exposure was 59.1%, 24.1%, and 47.2%, respectively. Diuretics (10%), insulin sliding scale (8.8%), amitriptyline (7.8%), and aspirin (6.9%) were among the most frequently prescribed PIMs. Older patients experiencing pain flare-ups were more likely to have multimorbidity (adjusted odds ratio (AOR): 1.64, 95% confidence intervals: 1.13–2.39). Persistent anger (AOR: 3.33; 1.71–6.47) and use of mobility aids (AOR: 2.41, 1.35–4.28) were associated with polypharmacy. Moreover, cognitive impairment (AOR: 1.65, 1.15–2.34) and health deterioration (AOR: 1.61, 1.11–2.32) increased the likelihood of PIM exposure. High prevalence of multimorbidity and PIM use was observed in Ethiopia. Several important determinants that can be modified by applying PIM criteria in routine practice were also identified.