We consider the problem of \textit{true} open-world semi-supervised node classification, in which nodes in a graph either belong to known or new classes, with the latter not present during training. Existing methods detect and reject new classes but fail to distinguish between different new classes. We adapt existing methods and show they do not solve the problem sufficiently. We introduce a novel end-to-end approach for classification into known classes and new classes based on class prototypes, which we call Prototypical Open-World Learning for Node Classification (POWN). Our method combines graph semi-supervised learning, self-supervised learning, and pseudo-labeling to learn prototype representations of new classes in a zero-shot way. In contrast to existing solutions from the vision domain, POWN does not require data augmentation techniques for node classification. Experiments on benchmark datasets demonstrate the effectiveness of POWN, where it outperforms baselines by up to 20% accuracy on the small and up to 30% on the large datasets. Source code is available at https://github.com/Bobowner/POWN.