The Talmud (Pesachim 76b) speaks about the danger of eating meat and fish together. The sages decreed a safeguard for health, and we do not cook or grill fish with meat either. Because grill racks are difficult to clean, different racks should be used for meat and fish, or one should wrap the fish in aluminum foil.
Note: A clean pot or pan that previously cooked meat can be used to cook fish.