Historical medical data of the patients have an important place in the healthcare industry for providing the best care to patients through intelligent health diagnosis and prediction of diseases. The existing intelligent health diagnosis systems collect data from medical institutions or laboratories and then use machine learning algorithms to predict diseases. But, in most cases, the medical institutions have incomplete medical data of the patients since a patient may consult different specialists (from various hospitals) during the treatment process. To overcome this problem, we build a smart and secure federated learning framework for intelligent health diagnosis with a blockchain-based incentive mechanism and NFT(Non-Fungible Tokens)-based marketplace. We make use of NFTs to develop clear demarkations on the ownership and accessibility of the data of patients. We create an NFT marketplace that manages access to the historical medical data of patients. A comprehensive incentive mechanism based on several factors, including the quality and relevance of the data, the frequency, and regularity of data uploading, etc., is incorporated to encourage and penalize the patients based on their contributions to the global model. We used the Polyak-averaging technique for aggregating local models to form a global model. The extensive analysis shows that the proposed model achieves comparable performance with the centralized machine learning models while affording better security and access to better data. The results also show the efficacy of the proposed blockchain-based incentive mechanism.