In modern life, the application of artificial intelligence (AI) has promoted the implementation of data-driven algorithms in high-stakes domains, such as healthcare. However, it is becoming increasingly challenging for humans to understand the working and reasoning of these complex and opaque algorithms. For AI to support essential decisions in these domains, specific ethical issues need to be addressed to prevent the misinterpretation of AI, which may have severe consequences for humans. However, little research has been published on guidelines that systematically addresses ethical issues when AI techniques are applied in healthcare. In this systematic literature review, we aimed to provide an overview of ethical concerns and related strategies that are currently identified when applying AI in healthcare. The review, which followed the PRISMA guidelines, revealed 12 main ethical issues: justice and fairness, freedom and autonomy, privacy, transparency, patient safety and cyber security, trust, beneficence, responsibility, solidarity, sustainability, dignity, and conflicts. In addition to these 12 main ethical issues, we derived 19 ethical sub-issues and associated strategies from the literature.