Healthcare institutions are progressively integrating artificial intelligence (AI) into their operations. The extraordinary potential of AI is restricted by insufficient medical data for AI model training and adversarial attacks wherein attackers perturb the dataset by adding some noise to it, which leads to the malfunctioning of the AI models, and a lack of trust caused by the opaque operational approach it employs. This Systematic Literature Review (SLR) is a state‐of‐the‐art survey of the research on blockchain technology for securing AI‐integrated healthcare applications. The most relevant articles from the Scopus and Web of Science (WoS) databases were identified using the PRISMA model. Most of the existing literature is about protecting the healthcare data used by AI‐based healthcare systems using blockchain technology, but the modality of data (text, images, audio, and sound) was not specifically mentioned. Information on protecting the training phase and model deployment for AI‐based healthcare systems considering the variations in feature extraction based on the modality of data was also not clearly specified. Hence, the three subfields of AI, namely, natural language processing (NLP), computer vision, and acoustic AI are further studied to identify security loopholes in its implementation pipeline. The three phases, namely the dataset, the training phase, and the trained models need to be protected from adversaries to avoid malfunctioning of the deployed AI models. The nature of the data processed by NLP, computer vision, and acoustic AI, underlying deep neural network (DNN) architectures, the complexity of attacks, and the perceivability of attacks by humans are analyzed to identify the need for security. A blockchain solution for AI‐based healthcare systems is synthesized based on the findings that have demonstrated the distinctive technological features of blockchains. It offers a solution for the privacy and security issues encountered by NLP, computer vision, and acoustic AI to boost the widespread adoption of AI applications in healthcare.