Hypertension (HTN) has a high prevalence in the overall population, affecting people’s mental health. Physical Activity (PA) has proven to be an effective tool to improve mental health. This study analyzed the associations between Depression and Anxiety prevalence, medication use for these disorders (antidepressants and anxiolytics) and Physical Activity Level (PAL) in people with HTN. A cross-sectional study was conducted with data from the Spanish National Health Survey 2017 (ENSE2017) with a final sample of 3228 individuals over 15 years of age with HTN who resided in Spain. Data normality was assessed through the Kolmogorov–Smirnov test. Associations between Depression and Anxiety prevalence, antidepressant and anxiolytic use and PAL were studied using a chi-square test. Possible differences between Depression and Anxiety prevalence and medication use according to the PAL were analyzed with a z-test for independent proportions. Depression or Anxiety and antidepressant and anxiolytic use odds ratios (OR) were calculated for every PAL group, taking the “Very Active” group as a reference. Risk factors were evaluated using multiple binary logistic regression. Dependency relationships were found between Depression and Anxiety prevalence, antidepressant and anxiolytic use and PAL (p < 0.001). The Inactive group displayed the highest prevalence and medication use according to their PAL (p < 0.05). Higher ORs for Depression or Anxiety and pharmacological treatments used were also found in the Inactive group compared to the other PAL groups.