Cellular regulatory mechanisms are typically governed by biochemical reaction networks. Discrete stochastic models are widely used in computational systems biology to analyze such networks. Often, the models involve a large number of highly uncertain parameters and many interacting chemical species. However, one is often interested in observing the output of one, or a few of the species rather than the entire network. Simulating the complete reaction network is inefficient in such cases. This paper explores the use of surrogate models to learn partial stochastic biochemical reaction networks and enable fast near-instant evaluation. The efficacy of the proposed method is demonstrated on a model from the systems biology literature.