Recent self-supervised learning methods are able to learn high-quality image representations and are closing the gap with supervised methods. However, these methods are unable to acquire new knowledge incrementally -- they are, in fact, mostly used only as a pre-training phase with IID data. In this work we investigate self-supervised methods in continual learning regimes without additional memory or replay. To prevent forgetting of previous knowledge, we propose the usage of functional regularization. We will show that naive functional regularization, also known as feature distillation, leads to low plasticity and therefore seriously limits continual learning performance. To address this problem, we propose Projected Functional Regularization where a separate projection network ensures that the newly learned feature space preserves information of the previous feature space, while allowing for the learning of new features. This allows us to prevent forgetting while maintaining the plasticity of the learner. Evaluation against other incremental learning approaches applied to self-supervision demonstrates that our method obtains competitive performance in different scenarios and on multiple datasets.