Provided are a method, system, and program for generating and indicating incremental backup copies from virtual copies of a data set. A virtual copy operation is initiated to create a virtual copy of a data set, wherein the virtual copy represents the data set at a point-in-time copy, and wherein the virtual copy is completed without transferring the data set to a backup location. An incremental backup operation is initiated with respect to an identified virtual copy, wherein the incremental backup operation copies changes to the data set that occur since a most recent creation of an incremental backup set.