Background: Hypertension is a major risk factor of cardiovascular disease and a leading cause of morbidity and mortality globally. In Kenya, the rise of hypertension strains an already stretched health care system that has traditionally focused on the management of infectious diseases. Health care provision in this country remains fragmented, and little is known about the role of health information technology in care coordination. Furthermore, there is a dearth of literature on the experiences, challenges, and solutions for improving the management of hypertension and other noncommunicable diseases in the Kenyan private health care sector. Objective: The aim of this study is to assess stakeholders' perspectives on the challenges associated with the management of hypertension in the Kenyan private health care sector and to derive recommendations for the design and functionality of a digital health solution for addressing the care continuity and quality challenges in the management of hypertension. Methods: We conducted a qualitative case study. We collected data using in-depth interviews with 18 care providers and 8 business leads, and direct observations at 18 private health care institutions in Nairobi, Kenya. We analyzed the data thematically to identify the key challenges and recommendations for technology-enabled solutions to support the management of hypertension in the Kenyan private health sector. We subsequently used the generated insights to derive and describe the design and range of functions of a digital health wallet platform for enabling care quality and continuity. Results: The management of hypertension in the Kenyan private health care sector is characterized by challenges such as high cost of care, limited health care literacy, lack of self-management support, ineffective referral systems, inadequate care provider training, and inadequate regulation. Care providers lack the tools needed to understand their patients' care histories and effectively coordinate efforts to deliver high-quality hypertension care. The proposed digital health platform was designed to support hypertension care coordination and continuity through clinical workflow orchestration, decision support, and patient-mediated data sharing with privacy preservation, auditability, and trust enabled by blockchain technology. Conclusions: The Kenyan private health care sector faces key challenges that require significant policy, organizational, and infrastructural changes to ensure care quality and continuity in the management of hypertension. Digital health data interoperability solutions are needed to improve hypertension care coordination in the sector. Additional studies should investigate how patients can control the sharing of their data while ensuring that care providers have a holistic view of the patient during any encounter.