In August 2024, the EU Artificial Intelligence Act (AI Act) entered into force. This legally binding instrument sets rules for the development, the placing on the market, the putting into service, and the use of AI systems in the European Union. As the world's first extensive legal framework on AI, it aims to boost innovation while protecting individuals against the harms of AI. Since healthcare is one of the top sectors for AI deployment, the new rules will significantly reform national policies and practices on health technology. In this article, we highlight the implications of the AI Act for the healthcare sector. We give a comprehensive overview of the new legal obligations for various healthcare stakeholders (tech developers; healthcare professionals; public health authorities). We conclude that, due to its horizontal approach, it is necessary to adopt further guidelines to address the unique needs of the healthcare sector. To this end, we make recommendations for the upcoming implementation and standardization phase.