Astrophysical transient phenomena are traditionally classified spectroscopically in a hierarchical taxonomy; however, this graph structure is currently not utilized in neural net-based photometric classifiers for time-domain astrophysics. Instead, independent classifiers are trained for different tiers of classified data, and events are excluded if they fall outside of these well-defined but flat classification schemes. Here, we introduce a weighted hierarchical cross-entropy objective function for classification of astrophysical transients. Our method allows users to directly build and use physics- or observationally-motivated tree-based taxonomies. Our weighted hierarchical cross-entropy loss directly uses this graph to accurately classify all targets into any node of the tree, re-weighting imbalanced classes. We test our novel loss on a set of variable stars and extragalactic transients from the Zwicky Transient Facility, showing that we can achieve similar performance to fine-tuned classifiers with the advantage of notably more flexibility in downstream classification tasks.