Provided are a computer program product, system, and method for using a machine learning module to select one of multiple cache eviction algorithms to use to evict a track from the cache. A first cache eviction algorithm determines tracks to evict from the cache. A second cache eviction algorithm determines tracks to evict from the cache, wherein the first and second cache eviction algorithms use different eviction schemes. At least one machine learning module is executed to produce output indicating one of the first cache eviction algorithm and the second cache eviction algorithm to use to select a track to evict from the cache. A track is evicted that is selected by one of the first and second cache eviction algorithms indicated in the output from the at least one machine learning module.