The industrial revolution of the 19th century marked the onset of an era of machines and robots that transformed societies. Since the beginning of the 21st century, a new generation of robots envisions similar societal transformation. These robots are biohybrid: part living and part engineered. They may self-assemble and emerge from complex interactions between living cells. While this new era of living robots presents unprecedented opportunities for positive societal impact, it also poses a host of ethical challenges. A systematic, nuanced examination of these ethical issues is of paramount importance to guide the evolution of this nascent field. Multidisciplinary fields face the challenge that inertia around collective action to address ethical boundaries may result in unexpected consequences for researchers and societies alike. In this Perspective, we i) clarify the ethical challenges associated with biohybrid robotics, ii) discuss the need for and elements of a potential governance framework tailored to this technology; and iii) propose tangible steps toward ethical compliance and policy formation in the field of biohybrid robotics.