In a small skillet pan over medium heat on the stove, melt the butter. Add the garlic and cook until soft, 2 to 3 minutes, stirring occasionally. Remove from the heat and add the remaining marinade ingredients. Stir and allow to cool to room temperature.
Place the shrimp in a large, resealable plastic bag and pour in the marinade. Press out the air and seal the bag tightly. Turn the bag to distribute the marinade, place in a bowl, and refrigerate for 20 to 30 minutes.
Prepare the grill for direct cooking over high heat (450° to 550°F).
Remove the shrimp from the bag and grill over direct high heat, with the lid closed, until just opaque in the center and firm to the touch, 2 to 4 minutes, turning once. Remove from the grill and serve warm or at room temperature.
