Machine learning methods have revolutionized the discovery process of new molecules and materials. However, the intensive training process of neural networks for molecules with ever increasing complexity has resulted in exponential growth in computation cost, leading to long simulation time and high energy consumption. Photonic chip technology offers an alternative platform for implementing neural network with faster data processing and lower energy usage compared to digital computers. Here, we demonstrate the capability of photonic neural networks in predicting the quantum mechanical properties of molecules. Additionally, we show that multiple properties can be learned simultaneously in a photonic chip via a multi-task regression learning algorithm, which we believe is the first of its kind, as most previous works focus on implementing a network for the task of classification. Photonics technology are also naturally capable of implementing complex-valued neural networks at no additional hardware cost and we show that such neural networks outperform conventional real-valued networks for molecular property prediction. Our work opens the avenue for harnessing photonic technology for large-scale machine learning applications in molecular sciences such as drug discovery and materials design.