Place the milk chocolate chips in a microwave-safe bowl and the white chocolate chips in another. Microwave one bowl on high for 1 minute. Remove and stir with a rubber spatula. (The chips should melt while you are stirring, but if they don't, you can continue to microwave for 15 more seconds, then stir again.) Wash and dry the spatula. Microwave the other bowl on high for 1 minute, and stir until the chocolate is melted.
Dip one pretzel rod into the milk chocolate; use a spoon or butter knife to spread the chocolate about halfway up the rod. Twist the rod to let the excess chocolate drip off. Hold the rod over a piece of wax paper and shake sprinkles on all sides. Place the pretzel on another piece of wax paper to dry. Coat another pretzel with white chocolate and sprinkles. Repeat until you've coated all the pretzels, half with milk chocolate, half with white chocolate, and let dry completely, about 24 hours. (Cover any remaining chocolate with plastic wrap and store in the refrigerator.)