(1) Background: Hypertension (HT) is the most common chronic condition, affecting approximately 1.13 billion people worldwide. Despite freely available blood pressure (BP) devices in primary care (PC) clinics, many patients do not regularly screen for HT and are untreated. (2) Methods: This study investigated the proportion of PC patients who did not screen for HT and the underlying reasons in Hong Kong. An explanatory mixed-method cross-sectional study was conducted in 2020, which included a questionnaire survey, office BP measurements, and subsequent semi-structured interviews. Adult patients who had no diagnosis of HT were recruited in a large PC clinic by convenience sampling. The relationships between not having HT screening and sociodemographic data were investigated by logistic regression. Twenty-four patients were purposefully sampled (based on demographics) and were interviewed until data saturation. (3) Results: Among 428 participants, 190 (44.4%) had not had HT screening in the last two years, but 197 (46.0%) had HT. No HT screening in the last two years or ever was associated with being male, being single, being of younger age, having no family history of HT, having no clinic visits in the last two years, employment status, and self-perceived HT condition. Most participants (77.8%) misinterpreted their BP readings. Individual, social, and healthcare service barriers were identified in patients’ interviews. Many PC patients had no regular HT screening but around half had elevated BP. (4) Conclusion: The study results indicate that the barriers to HT screening were multifactorial. HT screening in PC is urgently needed.