Light a grill or preheat a grill pan. In a small bowl, combine the lime zest and juice with the mint, garlic and the 1/4 cup of olive oil. Season with salt and pepper.
Alternately thread the zucchini, yellow squash and prosciutto onto 4 pairs of 12-inch bamboo skewers. Lightly brush the vegetables and prosciutto with olive oil and season generously with salt and pepper.
Grill the skewers over high heat until the zucchini and yellow squash are lightly charred, about 1 1/2 minutes per side. Serve with the mint dressing on the side.