In this work, we propose a fast adaptive federated meta-learning (FAM) framework for collaboratively learning a single global model, which can then be personalized locally on individual clients. Federated learning enables multiple clients to collaborate to train a model without sharing data. Clients with insufficient data or data diversity participate in federated learning to learn a model with superior performance. Nonetheless, learning suffers when data distributions diverge. There is a need to learn a global model that can be adapted using client's specific information to create personalized models on clients is required. MRI data suffers from this problem, wherein, one, due to data acquisition challenges, local data at a site is sufficient for training an accurate model and two, there is a restriction of data sharing due to privacy concerns and three, there is a need for personalization of a learnt shared global model on account of domain shift across client sites. The global model is sparse and captures the common features in the MRI. This skeleton network is grown on each client to train a personalized model by learning additional client-specific parameters from local data. Experimental results show that the personalization process at each client quickly converges using a limited number of epochs. The personalized client models outperformed the locally trained models, demonstrating the efficacy of the FAM mechanism. Additionally, the sparse parameter set to be communicated during federated learning drastically reduced communication overhead, which makes the scheme viable for networks with limited resources.