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Unfortunately this behavior is not natively implemented in Spinner component, however, you can always create your own BaseAdapter to show whatever you need weather is in the spinner it self or in the dropdown like this:

private class ExampleAdapter extends BaseAdapter{

                          @Override
                          public int getCount() {
                              return 0;
                          }

                          @Override
                          public Object getItem(int arg0) {
                              return null;
                          }

                          @Override
                          public long getItemId(int position) {
                              return 0;
                          }

                          @Override
                          public View getView(int position, View convertView, ViewGroup parent) {
                                          //Here is where you actually get the chance to return whatever you want in the spinner component (the single bar with the arrow)
                              return yourCommonView;
                          }

                          @Override
                          public View getDropDownView(int position, View convertView,
                                  ViewGroup parent) {
                                    //Here is where you get the chance to return whatever you want in the dropdown menu so here you should validate what's the currently selected element and return an image accordingly...
                              return yourSelectedView;
                          }

                      }

The important method here is, getDropDownView that is the one that gives you the chance to return an element with a checked CheckBox, or any mark you want to use, of course you have to create your own layout and validate if the element currently created need to be marked or not...

Regards!