Optimizing maritime operations, particularly fuel consumption for vessels, is crucial, considering its significant share in global trade. As fuel consumption is closely related to the shaft power of a vessel, predicting shaft power accurately is a crucial problem that requires careful consideration to minimize costs and emissions. Traditional approaches, which incorporate empirical formulas, often struggle to model dynamic conditions, such as sea conditions or fouling on vessels. In this paper, we present a hybrid, physics-guided neural network-based approach that utilizes empirical formulas within the network to combine the advantages of both neural networks and traditional techniques. We evaluate the presented method using data obtained from four similar-sized cargo vessels and compare the results with those of a baseline neural network and a traditional approach that employs empirical formulas. The experimental results demonstrate that the physics-guided neural network approach achieves lower mean absolute error, root mean square error, and mean absolute percentage error for all tested vessels compared to both the empirical formula-based method and the base neural network.