Demo of how to call MahApps dialogs from a view model, without knowledge of MetroWindow. MVVM framework agnostic.

C#: view model, attached property, and "coordinator"

 public partial class Mah : UserControl
    {
        public Mah()
        {
			DataContext = new MahViewModel();
            InitializeComponent();
        }
    }

	public class MahViewModel
	{
		private readonly ICommand _launchDialog;

		public MahViewModel()
		{
			_launchDialog = new AnotherCommandImplementation(_ => ShowDialog());
		}

		private void ShowDialog()
		{
			DialogCoordinator.ShowDialog(this);
		}

		public ICommand LaunchDialog
		{
			get { return _launchDialog; }
		}
	}

	public static class DialogCoordinator
	{
		public static Task<string> ShowDialog(object context)
		{
			if (context == null) throw new ArgumentNullException(nameof(context));
			if (!DialogParticipation.IsRegistered(context))
				throw new InvalidOperationException(
					"Context is not registered. Consider using DialogParticipation.Register in XAML to bind in the DataContext.");

			var association = DialogParticipation.GetAssociation(context);
			var metroWindow = Window.GetWindow(association) as MetroWindow;

			if (metroWindow == null)
				throw new InvalidOperationException("Control is not inside a MetroWindow.");

			return metroWindow.ShowInputAsync("From a VM", "This dialog was shown from a VM, without knoweldge of Window");
		}
	}

	public static class DialogParticipation
	{
		private static readonly IDictionary<object, DependencyObject> _contextRegistrationIndex = new Dictionary<object, DependencyObject>();

		public static readonly DependencyProperty RegisterProperty = DependencyProperty.RegisterAttached(
			"Register", typeof (object), typeof (DialogParticipation), new PropertyMetadata(default(object), RegisterPropertyChangedCallback));

		private static void RegisterPropertyChangedCallback(DependencyObject dependencyObject, DependencyPropertyChangedEventArgs dependencyPropertyChangedEventArgs)
		{
			//TODO tidy up old val?

			_contextRegistrationIndex[dependencyPropertyChangedEventArgs.NewValue] = dependencyObject;
		}

		public static void SetRegister(DependencyObject element, object context)
		{
			element.SetValue(RegisterProperty, context);
		}

		public static object GetRegister(DependencyObject element)
		{
			return element.GetValue(RegisterProperty);
		}

		internal static bool IsRegistered(object context)
		{
			if (context == null) throw new ArgumentNullException(nameof(context));

			return _contextRegistrationIndex.ContainsKey(context);
		}

		internal static DependencyObject GetAssociation(object context)
		{
			if (context == null) throw new ArgumentNullException(nameof(context));

			return _contextRegistrationIndex[context];
		}
	}

How to register for "participation" in the XAML

<UserControl x:Class="MahMaterialDragablzMashUp.Mah"
             xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
             xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
             xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006" 
             xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
             xmlns:controls="http://metro.mahapps.com/winfx/xaml/controls"
             xmlns:mahMaterialDragablzMashUp="clr-namespace:MahMaterialDragablzMashUp"
             mc:Ignorable="d" 
             d:DesignHeight="300" d:DesignWidth="300"
			 mahMaterialDragablzMashUp:DialogParticipation.Register="{Binding RelativeSource={RelativeSource Self}, Path=DataContext}"
			 >
</UserControl>

How does this actually get called from a metro window? As written, this will throw an exception since this is inside of a user control, not a metro window

@dasjestyr Make sure the windows inherits from type MetroWindow.