(1) Background: Genomic medicine harbors the real potential to improve the health and healthcare journey of patients, care provider experiences, and improve the health system efficiency—even reducing healthcare costs. There is expected to be an exponential growth in medically necessary new genome-based tests and test approaches in the coming years. Testing can also create scientific research and commercial opportunities beyond healthcare decision making. The purpose of this research is to generate a better understanding of Canada’s state of readiness for genomic medicine, and to provide some insights for other healthcare systems. (2) Methods: A mixed-methods approach of a review of the literature and key informant interviews with a purposive sample of experts was used. The health system readiness was assessed using a previously published set of conditions. (3) Results: Canada has created some of the established conditions, but further action needs to be taken to improve the state of readiness for genome-based medicine. The important gaps to be filled are the need for linked information systems and data integration; evaluative processes that are timely and transparent; navigational tools for care providers; dedicated funding to facilitate rapid onboarding and support test development and proficiency testing; and broader engagement with innovation stakeholders beyond care providers and patients. These findings highlight the role of the organizational context, social influence, and other factors that are known to affect the diffusion of innovation within health systems.