Provided are a computer program product, system, and method for generating a health condition message on a health condition detected at a first server to send to a host system accessing the first server. A determination is made of a health condition with respect to access to a first storage. A determination is made of an estimated Input/Output (I/O) delay to access the first storage resulting from the determined health condition. A health condition message is generated indicating the estimated I/O delay. The health condition message is transmitted to the host system, wherein the host system uses the estimated I/O delay to determine whether to perform a swap operation to redirect host I/O requests to data from the first server to a second server.