With help of Jeroen, I got it sorted: VPP will not work in precompiled apps ( https://twitter.com/crumpled_jeavon/status/832563262218711040 ) without hacks ( https://github.com/JimBobSquarePants/UmbracoFileSystemProviders.Azure/issues/37 ). So, I took https://sunali.com/2008/01/09/virtualpathprovider-in-precompiled-web-sites/ as a base and added following code in our RegisterEvents class, which is inherited from ApplicationEventHandler, in ApplicationStarting method

   private void HackishlyRegisterVpp()
    {
        if (!BuildManager.IsPrecompiledApp)
        {
            //we do not need to register VPP if web app is not precompiled
            return;
        }
        var fs = FileSystemProviderManager.Current.GetUnderlyingFileSystemProvider("media");
        Lazy<IFileSystem> fileSystem = new Lazy<IFileSystem>((Func<IFileSystem>)(() => fs));
        // we create a new instance of our own VirtualPathProvider.
        var providerInstance = new Our.Umbraco.FileSystemProviders.Azure.FileSystemVirtualPathProvider("media", fileSystem);
        // any settings about your VirtualPathProvider may go here.

        // we get the current instance of HostingEnvironment class. We can't create a new one
        // because it is not allowed to do so. An AppDomain can only have one HostingEnvironment
        // instance.
        HostingEnvironment hostingEnvironmentInstance = (HostingEnvironment)typeof(HostingEnvironment).InvokeMember("_theHostingEnvironment", BindingFlags.NonPublic | BindingFlags.Static | BindingFlags.GetField, null, null, null);
        if (hostingEnvironmentInstance == null)
        {
            return;
        }

        // we get the MethodInfo for RegisterVirtualPathProviderInternal method which is internal
        // and also static.
        MethodInfo mi = typeof(HostingEnvironment).GetMethod("RegisterVirtualPathProviderInternal", BindingFlags.NonPublic | BindingFlags.Static);
        if (mi == null)
        {
            return;
        }

        // finally we invoke RegisterVirtualPathProviderInternal method with one argument which
        // is the instance of our own VirtualPathProvider.
        mi.Invoke(hostingEnvironmentInstance, new object[] { (VirtualPathProvider)providerInstance });
    }