string Image = "https://fbcdn-profile-a.akamaihd.net/hprofile-ak-prn2/187738_100000230436565_1427264428_q.jpg";

<Image Name="img" HorizontalAlignment="Left" VerticalAlignment="Top" Width="66" Height="66" Source="{Binding Image} " />

var bitmapImage = new BitmapImage();
bitmapImage.BeginInit();
bitmapImage.UriSource = new Uri("https://fbcdn-profile-a.akamaihd.net/hprofile-ak-prn2/187738_100000230436565_1427264428_q.jpg");;
bitmapImage.EndInit();

img.Source = bitmapImage;

var imgUrl = new Uri("https://fbcdn-profile-a.akamaihd.net/hprofile-ak-prn2/187738_100000230436565_1427264428_q.jpg");
var imageData = new WebClient().DownloadData(imgUrl);

// or you can download it Async won't block your UI
// var imageData = await new WebClient().DownloadDataTaskAsync(imgUrl);

var bitmapImage = new BitmapImage {CacheOption = BitmapCacheOption.OnLoad};
bitmapImage.BeginInit();
bitmapImage.StreamSource = new MemoryStream(imageData);
bitmapImage.EndInit();

return bitmapImage;