Provided are a computer program product, system, and method for non-disruptive encoding of source data in a source data set migrated to a target data set. The source data in the source data set is migrated to a target data set by encoding the source data to produce encoded source data to copy to a target data set. In response to receiving write data for the source data set, the write data is encoded to produce encoded write data to copy to the target data set. Input/Output (“I/O”) requests to the source data set are redirected to the target data set having encoded data for the source data set.