Soak the skewers: If using wooden skewers, soak in water while preparing the shrimp.
Make the marinade: Combine the yogurt, lemon juice, garlic, and mint in a large bowl.
Marinate the shrimp: Add the shrimp to the yogurt mixture and toss to coat. Cover and refrigerate for 30 minutes. Meanwhile, prepare the grill.
Prepare the grill for direct heat: Heat half of the burners of a gas grill to high or prepare a chimney’s worth of lump charcoal for a charcoal grill. Make sure that the grill grates are clean and debris-free. Preheat the gas grill for at least 10 minutes.
Skewer the shrimp: Thread the shrimp onto the skewers, leaving any yogurt that clings to the shrimp. Skewer through the thickest part of each shrimp, arranging 6 to 8 shrimp per skewer. Place on a large plate or baking sheet.
Grill the shrimp: Grill the shrimp over direct heat for about 2 minutes per side, flipping as soon as the first side begins to turn pink along the edges. Cook until the shrimp are opaque and slightly charred.