Artificial Neural Networks (NNs) are unable to learn tasks continually using a single model, which leads to forgetting old knowledge, known as catastrophic forgetting. This is one of the shortcomings that usually plague intelligent systems based on NN models. Federated Learning (FL) is a decentralized approach to training machine learning models on multiple local clients without exchanging raw data. A paradigm that handles model learning in both settings, federated and continual, is known as Federated Continual Learning (FCL). In this work, we propose a novel FCL algorithm, called FedCluLearn, which uses a stream micro-cluster indexing scheme to deal with catastrophic forgetting. FedCluLearn interprets the federated training process as a stream clustering scenario. It stores statistics, similar to micro-clusters in stream clustering algorithms, about the learned concepts at the server and updates them at each training round to reflect the current local updates of the clients. FedCluLearn uses only active concepts in each training round to build the global model, meaning it temporarily forgets the knowledge that is not relevant to the current situation. In addition, the proposed algorithm is flexible in that it can consider the age of local updates to reflect the greater importance of more recent data. The proposed FCL approach has been benchmarked against three baseline algorithms by evaluating its performance in several control and real-world data experiments. The implementation of FedCluLearn and the experimental results are available at https://github.com/milenaangelova1/FedCluLearn.