Crush the peaches until they release some of their juice, leaving a few small chunks.
In the large mixing bowl, whisk together the Greek yogurt, whipping cream, sugar, and vanilla extract until thoroughly combined. Stir in the peaches until well mixed.
Pour into the popsicle molds and insert sticks. Freeze until firm, at least 4 hours. Run some warm water over the molds to release the popsicles. Wrap leftover popsicles in wax paper and store in a freezer bag. Popsicles will keep for about 2 weeks in the freezer.