Background: Investigating the factors associated with unmet medical needs is important since it can reflect access to healthcare. This study examined the relationship between the unmet medical needs of patients with hypertension and their satisfaction with the healthcare services available in their neighborhoods. Methods: Data were from the 2021 Korean Community Health Survey. The sample included individuals aged 19 years who were diagnosed with hypertension. The main outcome measure was unmet medical need. The relationship between the outcome measure and independent variables were analyzed using multivariate logistic regressions, along with a subgroup analysis based on whether patients were currently receiving treatment for hypertension. Results: Unmet medical needs were found in 4.3% of the study participants. A higher likelihood of unmet medical needs was found in individuals not satisfied with the healthcare services at proximity (adjusted OR = 1.69, 95% CI: 1.49–1.92) compared to those satisfied with services nearby. Similar tendencies were found regardless of whether individuals were currently receiving treatment for hypertension, although larger differences were found between groups in participants who were currently not receiving treatment. Conclusions: The findings infer the need to consider patient satisfaction with nearby healthcare services in implementing public health policies that address unmet medical need in patients with hypertension.