An apparatus in one embodiment comprises a distributed data processing system in which multiple processing devices communicate with one another over at least one network. The distributed data processing system is configured to obtain reads of biological samples of respective microbiomes, with each of the biological samples containing genomic material from a plurality of distinct microorganisms of its corresponding one of the microbiomes, and to perform distributed data analytics to detect a disease, infection or contamination that involves genomic material from multiple ones of the distinct microorganisms in one or more of the microbiomes. Performing distributed data analytics illustratively comprises performing local analytics in respective ones of a plurality of data zones, and performing global analytics utilizing results of the local analytics performed in the respective data zones. Each of the data zones may comprise, for example, one or more sequencing centers utilized to generate a corresponding subset of the reads within that data zone.