Efficient processing of large-scale time-series data is an intricate problem in machine learning. Conventional sensor signal processing pipelines with hand-engineered feature extraction often involve huge computational costs with high dimensional data. Deep recurrent neural networks have shown promise in automated feature learning for improved time-series processing. However, generic deep recurrent models grow in scale and depth with the increased complexity of the data. This is particularly challenging in presence of high dimensional data with temporal and spatial characteristics. Consequently, this work proposes a novel deep cellular recurrent neural network (DCRNN) architecture to efficiently process complex multidimensional time-series data with spatial information. The cellular recurrent architecture in the proposed model allows for location-aware synchronous processing of time-series data from spatially distributed sensor signal sources. Extensive trainable parameter sharing due to cellularity in the proposed architecture ensures efficiency in the use of recurrent processing units with high-dimensional inputs. This study also investigates the versatility of the proposed DCRNN model for the classification of multiclass time-series data from different application domains. Consequently, the proposed DCRNN architecture is evaluated using two time-series data sets: a multichannel scalp electroencephalogram (EEG) data set for seizure detection, and a machine fault detection data set obtained in-house. The results suggest that the proposed architecture achieves state-of-the-art performance while utilizing substantially less trainable parameters when compared to comparable methods in the literature.