It's possible to use Web.config Transformations for App.config files through a workaround.
You simply have to invoke the appropriate MSBuild tasks at the right stage in your build process.
Add this code snippet to your project file:
<UsingTask
    TaskName="TransformXml"
    AssemblyFile="$(MSBuildExtensionsPath32)\Microsoft\VisualStudio\v10.0\Web\Microsoft.Web.Publishing.Tasks.dll" />
<Target Name="AfterCompile" Condition="exists('App.$(Configuration).config')">
    <!-- Generates the transformed App.config in the intermediate directory -->
    <TransformXml
        Source="App.config"
        Destination="$(IntermediateOutputPath)$(TargetFileName).config"
        Transform="App.$(Configuration).config" />
    <!-- Forces the build process to use the transformed configuration file -->
    <ItemGroup>
        <AppConfigWithTargetPath Remove="App.config"/>
        <AppConfigWithTargetPath
            Include="$(IntermediateOutputPath)$(TargetFileName).config">
            <TargetPath>$(TargetFileName).config</TargetPath>
        </AppConfigWithTargetPath>
    </ItemGroup>
</Target>
Then add additional App.config files to your project for each build configuration where you wish to apply a transformation. For example:
<ItemGroup>
    <None Include="App.config" />
    <None Include="App.Release.config">
        <DependentUpon>App.config</DependentUpon>
    </None>
</ItemGroup>
Related resources: