Remove grapes from the stalk. Set 1 cup grapes aside. Put the rest into a food processor or blender and blend until smooth. Strain the mixture, discarding the skin. You should have 2 cups juice.
Whisk the grape juice and yoghurt together in a large container suitable for the freezer. Add the ice cream and whisk until well combined. Freeze for 1 hour. Remove from freezer, whisk until smooth and freeze further 1 hour.
Remove from freezer, whisk until smooth. Cut any of the large reserved grapes in half, then stir all grapes into ice cream mixture. Spoon into popsicle molds. Position stick in the centre, cover and freeze overnight. Remove popsicles from the molds to serve.