Beat milk and pudding mix together with a wire whisk in a saucepan until powder is dissolved into liquid; bring to a full, rolling boil and remove immediately from heat. Let pudding cool slightly, about 10 minutes.
Fold whipped topping into the pudding mixture; add cookies and stir. Pour the mixture into ice pop molds.
Put molds in freezer until the pudding mixture is firm, 4 to 5 hours.