Unmet medical needs refer to the state where a patient’s medical care or service is insufficient, inadequate, or lacking. Numerous factors influence unmet medical needs. We used a multi-pronged approach to explore the factors influencing unmet medical needs in the Korean health care system according to Anderson’s Behavioral Model of Health Services Use. To this end, we used data from 11,378 adults over 19 years old in the 2016 Korea Health Panel Survey and performed multiple logistic regression analyses. The odds of experiencing unmet medical needs were significantly greater among older participants (odds ratio (OR) = 2.51, 95% confidence interval (CI) = 1.78–3.56); low-income participants (OR = 1.41, 95% CI = 1.14–1.75); non-workers (OR = 1.24, 95% CI = 1.06–1.46); those who had received non-covered treatment (OR = 1.24, 95% CI = 1.08–1.42); those who did not regularly exercise (OR = 1.23, 95% CI = 1.02–1.48); and those experiencing pain (OR = 2.29, 95% CI = 1.97–2.66), worse self-rated health status (OR = 2.29, 95% CI = 1.89–2.79), and severe depression (OR = 2.46, 95% CI = 1.39–4.35). About one in ten Korean citizens (11.60%) have unmet medical service needs. Policies that strengthen coverage for physically and economically vulnerable groups are needed.