During the COVID-19 pandemic, telehealth has played a prominent role in the treatment of hepatitis C. As part of a qualitative study on the accessibility and effectiveness of telehealth for hepatitis C treatment during this period in Australia, this article considers how health-care practitioners and patients experience and manage their proximity to each other in telehealth encounters of care. Comparisons between telehealth and in-person health-care tend to focus on measures of patient satisfaction rather than qualitative changes in treatment relationships. Media scholar Silverstone (Digital media revisited: Theoretical and conceptual innovations in digital domains, MIT Press, 2003) uses the term ‘proper distance’ to theorise how ethical relationships are mediated by technology. Drawing on this concept, we explore how patients and health-care practitioners understand telehealth as affecting distance and proximity. We find that both groups express some ambivalence about the impact of telehealth on relationships, on the one hand expecting and privileging simple, transactional relationships, and on the other hand, expressing concerns about the loss of more intimate relationships in health care and about ‘missing something’ while providing health care. Given that proximity is important to the development of ethical relationships in health care, we conclude with some considerations for establishing and sustaining attentive and responsive relationships in telehealth.