This paper presents an external wrench estimator that uses a hybrid dynamics model consisting of a first-principles model and a neural network. This framework addresses one of the limitations of the state-of-the-art model-based wrench observers: the wrench estimation of these observers comprises the external wrench (e.g. collision, physical interaction, wind); in addition to residual wrench (e.g. model parameters uncertainty or unmodeled dynamics). This is a problem if these wrench estimations are to be used as wrench feedback to a force controller, for example. In the proposed framework, a neural network is combined with a first-principles model to estimate the residual dynamics arising from unmodeled dynamics and parameters uncertainties, then, the hybrid trained model is used to estimate the external wrench, leading to a wrench estimation that has smaller contributions from the residual dynamics, and affected more by the external wrench. This method is validated with numerical simulations of an aerial robot in different flying scenarios and different types of residual dynamics, and the statistical analysis of the results shows that the wrench estimation error has improved significantly compared to a model-based wrench observer using only a first-principles model.