I got from https://github.com/dotnet/corefx/issues/3633, that XSD Schema Validation now is not yet supported, and planned in .Net Core 1.2.0 whose release date
.Net Core 1.2.0
If you need some functionality that needs to be run in .Net Core library, you may try to port your product with portable library workaround.
.Net Core
However, it's nearly the .NET Core 2.0 Preview time, so you may basically wait for it.