With rapid advances of deep neural networks over the past decade, artificial intelligence (AI) systems are now commonplace in many applications in biomedicine. These systems often achieve high predictive accuracy in clinical studies, and increasingly in clinical practice. Yet, despite their commonly high predictive accuracy, the trustworthiness of AI systems needs to be questioned when it comes to decision-making that affects the well-being of patients or the fairness towards patients or other stakeholders affected by AI-based decisions. To address this, the field of explainable artificial intelligence, or XAI for short, has emerged, seeking to provide means by which AI-based decisions can be explained to experts, users, or other stakeholders. While it is commonly claimed that explanations of artificial intelligence (AI) establish the trustworthiness of AI-based decisions, it remains unclear what traits of explanations cause them to foster trustworthiness. Building on historical cases of scientific explanation in medicine, we here propagate our perspective that, in order to foster trustworthiness, explanations in biomedical AI should meet the criteria of being scientific explanations. To further undermine our approach, we discuss its relation to the concepts of causality and randomized intervention. In our perspective, we combine aspects from the three disciplines of biomedicine, machine learning, and philosophy. From this interdisciplinary angle, we shed light on how the explanation and trustworthiness of artificial intelligence relate to the concepts of causality and robustness. To connect our perspective with AI research practice, we review recent cases of AI-based studies in pathology and, finally, provide guidelines on how to connect AI in biomedicine with scientific explanation.