Store for Up to Four Days
Fish soup must be refrigerated after it is cooked. According to Katherine Zeratsky, a nutritionist at the Mayo Clinic, all refrigerated foods should be eaten within four days of storing them.
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Fish Spoils Faster than Other Foods
Fish and foods cooked with fish are not a normal leftover because they can spoil faster than other foods. Experts at Boecker Food Safety say "Never store fish in the refrigerator for more than a day." This time can be extended slightly if the fish or fish dish is stored on ice in the fridge.
Storing fish soup makes sense for up to four days under normal circumstances but this can change depending on the expiration date of the fish used to make the soup.