Defects in additively manufactured materials are one of the leading sources of uncertainty in mechanical fatigue. Fracture mechanics concepts are useful to evaluate their influence, nevertheless, these approaches cannot account for the real morphology of defects. Preliminary attempts to exploit a more comprehensive description of defects can be found in the literature, by using Machine Learning. These approaches are notoriously data-hungry and neither physics laws nor phenomenological rules are introduced to assess the soundness of the outcome. Hereby, to overcome this limitation, an approach to predicting fatigue finite life of defective materials, based on a Physics-Informed Neural Network framework, is presented for the first time. The training process of a Neural Network is reinforced by introducing novel Fracture Mechanics constraints. Experimental results obtained from the literature, including detailed defect analysis from computer tomography and fractography, were used to check its accuracy. The proposed predictive tool fully exploits the advanced capabilities of machine learning to account for morphological aspects of defects that could not be accounted for otherwise, while at the same time obeying fracture mechanics laws and requiring a smaller experimental dataset. The approach paves the way for new structural design approaches with an unprecedented degree of accuracy.