Microarray technology allows for the simultaneous monitoring of thousands of genes expressions per sample. Unfortunately, the classification of these samples into distinct classes is often difficult as the number of genes (features) greatly exceeds the number of samples. Consequently, there is a need to investigate new, robust machine learning techniques capable of accurately classifying microarray data. In this paper, we present a coevolutionary learning classifier system based on feature set partitioning to classify gene expression data. A distributed implementation, which leverages Cloud computing technologies, is used to address the inherent computational costs of our model. The development and execution of this application was done using the Aneka middleware on the public Cloud (Amazon EC2) infrastructure. Experiments conducted using gene expression profiles demonstrates that the proposed implementation outperforms other well-known classifiers in terms of accuracy. Preliminary analysis into the impact of different Cloud setups on the performance of the classifier are also reported.