Provided are a computer program product, system, and method for using at least one machine learning module to select a priority queue from which to process an Input/Output (I/O) request. Input I/O statistics are provided on processing of I/O requests at the queues to at least one machine learning module. Output is received from the at least one machine learning module for each of the queues. The output for each queue indicates a likelihood that selection of an I/O request from the queue will maintain desired response time ratios between the queues. The received output for each of the queues is used to select a queue of the queues. An I/O request from the selected queue is processed.