Combine shrimp, olive oil, paprika, chili powder, and cumin in a large bowl. Gently stir until evenly combined. Cover and refrigerate while you prepare the salsa.
Preheat an outdoor grill for medium-high heat and lightly oil the grate. Grill tomatoes, onion, garlic, and jalapeno for 4 minutes. Flip and grill until tomatoes and jalapenos are blistered, about 4 minutes more.
Cut tops off the tomatoes and discard. Cut jalapeno in half, scrape the skin off, and discard seeds. Quarter the onion. Squeeze garlic cloves from their skins.
Place the grilled vegetables in a blender. Add lime juice and salt; blend until smooth. Add cilantro and pulse until evenly blended.
Transfer shrimp to the hot grill and cook for 2 minutes per side. Serve with the salsa.