Higher-order sensor networks are more accurate in characterizing the nonlinear dynamics of sensory time-series data in modern industrial settings by allowing multi-node connections beyond simple pairwise graph edges. In light of this, we propose a deep spatio-temporal hypergraph convolutional neural network for soft sensing (ST-HCSS). In particular, our proposed framework is able to construct and leverage a higher-order graph (hypergraph) to model the complex multi-interactions between sensor nodes in the absence of prior structural knowledge. To capture rich spatio-temporal relationships underlying sensor data, our proposed ST-HCSS incorporates stacked gated temporal and hypergraph convolution layers to effectively aggregate and update hypergraph information across time and nodes. Our results validate the superiority of ST-HCSS compared to existing state-of-the-art soft sensors, and demonstrates that the learned hypergraph feature representations aligns well with the sensor data correlations. The code is available at https://github.com/htew0001/ST-HCSS.git