Heat the blueberries and honey in a small saucepan over medium heat. Simmer until the blueberries release their juices; 4 to 5 minutes. Mash the blueberries with a fork and let them cool.
Whisk the yogurt, lemon juice, and milk together.
Fold the cooled blueberry mixture into the yogurt. For a marbled effect, stir only a couple of times so there are streaks of color. For a solid color, blend until mixed thoroughly.
Pour the mixture into six 3-ounce popsicle molds. Place the sticks into the molds, cover, and freeze for at least 3 hours or overnight. To unmold, run the mold under warm water before pulling the popsicles out.