In May, 2017 I wrote this article which describes how to include the XML documentation in your publish output.
Outdated
My latest approach (for the sake of completeness) was (add to your csproj file):
<Target Name="PrepublishScript" BeforeTargets="PrepareForPublish">
<ItemGroup>
<DocFile Include="bin\$(Configuration)\$(TargetFramework)\$(RuntimeIdentifier)\$(TargetName).xml" />
</ItemGroup>
<Copy SourceFiles="@(DocFile)" DestinationFolder="$(PublishDir)" SkipUnchangedFiles="false" />
</Target>
<PropertyGroup Condition="'$(Configuration)|$(Platform)'=='Debug|AnyCPU'">
<DocumentationFile>bin\Debug\netcoreapp2.0\YOURPROJECT.xml</DocumentationFile>
</PropertyGroup>
<PropertyGroup Condition="'$(Configuration)|$(Platform)'=='Release|AnyCPU'">
<DocumentationFile>bin\Release\netcoreapp2.0\YOURPROJECT.xml</DocumentationFile>
</PropertyGroup>
New and easier approach
But now you can just use
<PropertyGroup>
<GenerateDocumentationFile>true</GenerateDocumentationFile>
</PropertyGroup>
in your project file and visual studio takes care of debug/release folders and publishes your xml.
Solution found in this github issue.
Edit: This solution is still valid for .netcore3.1